Data Analysis and Prediction for Life Expectancy
Group 106: Artsiom Strok, Lin Jiang, Mayank Chhablani
July 15, 2019
Introduction
Life expectancy has increased dramatically over the last few centuries. Since 1900 the global average life expectancy has more than doubled and there has been a huge development in health sector in the past 15 years resulting in improvement of human mortality rates especially in the developing nations in comparison to the past 30 years. Therefore, in this project, only data from year 2000-2015 is considered for exploration and analysis.
This dataset is a compilation of data from the Global Health Observatory (GHO) and United Nations. The GHO data repository is WHO’s gateway to health-related statistics which provides access to a variety of indicators on priority health topics including mortality and burden of diseases, environmental health, violence and injuries etc. (http://apps.who.int/gho/data/node.resources). The economic data such as GDP is collected from the National Accounts Main Aggregates Database under United Nations which collects and disseminates economic statistics from countries worldwide (https://unstats.un.org/unsd/snaama/Index).
This dataset is cleaned by removing some missing values, maily for population, Hepatitis B and GDP from less known countries and shared on Kaggle website (https://www.kaggle.com/kumarajarshi/life-expectancy-who). The final dataset contains 2938 observations with 22 variables which are more critical and representative among all the categories of health-related factors from year 2000 - 2015 for 193 countries.
The description of each variable for this dataset is listed below:
- Country: Country
- Year: Year
- Status: Developed or Developing status
- Life expectancy: Life Expectancy in age
- Adult Mortality: Adult Mortality Rates of both sexes (probability of dying between 15 and 60 years per 1000 population)
- infant: deathsNumber of Infant Deaths per 1000 population
- Alcohol: Alcohol, recorded per capita (15+) consumption (in litres of pure alcohol)
- percentage expenditure: Expenditure on health as a percentage of Gross Domestic Product per capita(%)
- Hepatitis B: Hepatitis B (HepB) immunization coverage among 1-year-olds (%)
- Measles: Measles - number of reported cases per 1000 population
- BMI: Average Body Mass Index of entire population
- under-five deaths: Number of under-five deaths per 1000 population
- Polio: Polio (Pol3) immunization coverage among 1-year-olds (%)
- Total expenditure: General government expenditure on health as a percentage of total government expenditure (%)
- Diphtheria: Diphtheria tetanus toxoid and pertussis (DTP3) immunization coverage among 1-year-olds (%)
- HIV/AIDS: Deaths per 1 000 live births HIV/AIDS (0-4 years)
- GDP: Gross Domestic Product per capita (in USD)
- Population: Population of the country
- thinness 1-19 years: Prevalence of thinness among children and adolescents for Age 10 to 19 (% )
- thinness 5-9 years: Prevalence of thinness among children for Age 5 to 9(%)
- Income composition of resources: Human Development Index in terms of income composition of resources (index ranging from 0 to 1)
- Schooling: Number of years of Schooling(years)
For this project, we would like to:
- identify the major factors that affect the life expectancy
- explore the interactions between the variables such as immunization, moratlity, education, economic factors etc.
- discover the corelation between different factors
- perform residual and outlier diagnostics to exclude some influential points if any
- build a robust multiple linear regression model to predict the life expectancy
- build a classifier to estimate the status of a country (developing or developed)
Methods
Missing values analysis:
original_data = read.csv("Life Expectancy Data.csv")
kable(t(original_data[sample(nrow(original_data), 5), ]))| 2609 | 2369 | 1177 | 1098 | 1252 | |
|---|---|---|---|---|---|
| Country | Timor-Leste | Solomon Islands | Iceland | Guinea-Bissau | Ireland |
| Year | 2008 | 2008 | 2009 | 2008 | 2014 |
| Status | Developing | Developing | Developed | Developing | Developed |
| Life.expectancy | 66.2 | 68.0 | 81.6 | 55.6 | 81.2 |
| Adult.Mortality | 168 | 193 | 55 | 297 | 66 |
| infant.deaths | 2 | 0 | 0 | 5 | 0 |
| Alcohol | 0.06 | 1.09 | 10.22 | 2.64 | 10.75 |
| percentage.expenditure | 36.69 | 19.75 | 687.58 | 28.30 | 746.37 |
| Hepatitis.B | 79 | 89 | NA | NA | 95 |
| Measles | 0 | 0 | 0 | 12 | 33 |
| BMI | 14.7 | 44.7 | 58.5 | 21.9 | 62.1 |
| under.five.deaths | 3 | 0 | 0 | 7 | 0 |
| Polio | 79 | 94 | 96 | 77 | 96 |
| Total.expenditure | 0.74 | 5.97 | 9.12 | 6.50 | 7.78 |
| Diphtheria | 79 | 89 | 96 | 77 | 96 |
| HIV.AIDS | 0.1 | 0.1 | 0.1 | 6.0 | 0.1 |
| GDP | 643.7 | 125.8 | 4461.9 | 583.5 | 5553.3 |
| Population | 17811 | 54477 | 318499 | 148841 | 4617225 |
| thinness..1.19.years | 11.7 | 1.2 | 0.9 | 8.5 | 0.3 |
| thinness.5.9.years | 11.7 | 1.2 | 0.9 | 8.4 | 0.2 |
| Income.composition.of.resources | 0.566 | 0.489 | 0.894 | 0.398 | 0.910 |
| Schooling | 11.7 | 9.2 | 18.4 | 8.8 | 18.6 |
kable(colSums(is.na(original_data)), col.names = "Number of missing values")| Number of missing values | |
|---|---|
| Country | 0 |
| Year | 0 |
| Status | 0 |
| Life.expectancy | 10 |
| Adult.Mortality | 10 |
| infant.deaths | 0 |
| Alcohol | 194 |
| percentage.expenditure | 0 |
| Hepatitis.B | 553 |
| Measles | 0 |
| BMI | 34 |
| under.five.deaths | 0 |
| Polio | 19 |
| Total.expenditure | 226 |
| Diphtheria | 19 |
| HIV.AIDS | 0 |
| GDP | 448 |
| Population | 652 |
| thinness..1.19.years | 34 |
| thinness.5.9.years | 34 |
| Income.composition.of.resources | 167 |
| Schooling | 163 |
1289 samples have at least one missing value. Alcohol is missing in 194 samples all of them belongs to 2015 year and these countiries definately should have alcohol consuption more than 0. The data was collected in 2015 when data about alcohol consumption simply was not available.
Life expextancy and adult mortality is missing for 10 samples in 2013, all of them belongs to islands.
Hepatitis B is missing in 553 samples. Samples belongs to different countries and years.
nrow(original_data)## [1] 2938data = na.omit(original_data)
nrow(original_data) - nrow(data)## [1] 1289summary(data)## Country Year Status Life.expectancy
## Afghanistan: 16 Min. :2000 Developed : 242 Min. :44.0
## Albania : 16 1st Qu.:2005 Developing:1407 1st Qu.:64.4
## Armenia : 15 Median :2008 Median :71.7
## Austria : 15 Mean :2008 Mean :69.3
## Belarus : 15 3rd Qu.:2011 3rd Qu.:75.0
## Belgium : 15 Max. :2015 Max. :89.0
## (Other) :1557
## Adult.Mortality infant.deaths Alcohol percentage.expenditure
## Min. : 1 Min. : 0.0 Min. : 0.01 Min. : 0
## 1st Qu.: 77 1st Qu.: 1.0 1st Qu.: 0.81 1st Qu.: 37
## Median :148 Median : 3.0 Median : 3.79 Median : 145
## Mean :168 Mean : 32.6 Mean : 4.53 Mean : 699
## 3rd Qu.:227 3rd Qu.: 22.0 3rd Qu.: 7.34 3rd Qu.: 509
## Max. :723 Max. :1600.0 Max. :17.87 Max. :18961
##
## Hepatitis.B Measles BMI under.five.deaths
## Min. : 2.0 Min. : 0 Min. : 2.0 Min. : 0.0
## 1st Qu.:74.0 1st Qu.: 0 1st Qu.:19.5 1st Qu.: 1.0
## Median :89.0 Median : 15 Median :43.7 Median : 4.0
## Mean :79.2 Mean : 2224 Mean :38.1 Mean : 44.2
## 3rd Qu.:96.0 3rd Qu.: 373 3rd Qu.:55.8 3rd Qu.: 29.0
## Max. :99.0 Max. :131441 Max. :77.1 Max. :2100.0
##
## Polio Total.expenditure Diphtheria HIV.AIDS
## Min. : 3.0 Min. : 0.74 Min. : 2.0 Min. : 0.10
## 1st Qu.:81.0 1st Qu.: 4.41 1st Qu.:82.0 1st Qu.: 0.10
## Median :93.0 Median : 5.84 Median :92.0 Median : 0.10
## Mean :83.6 Mean : 5.96 Mean :84.2 Mean : 1.98
## 3rd Qu.:97.0 3rd Qu.: 7.47 3rd Qu.:97.0 3rd Qu.: 0.70
## Max. :99.0 Max. :14.39 Max. :99.0 Max. :50.60
##
## GDP Population thinness..1.19.years thinness.5.9.years
## Min. : 2 Min. :3.40e+01 Min. : 0.10 Min. : 0.10
## 1st Qu.: 462 1st Qu.:1.92e+05 1st Qu.: 1.60 1st Qu.: 1.70
## Median : 1593 Median :1.42e+06 Median : 3.00 Median : 3.20
## Mean : 5566 Mean :1.47e+07 Mean : 4.85 Mean : 4.91
## 3rd Qu.: 4719 3rd Qu.:7.66e+06 3rd Qu.: 7.10 3rd Qu.: 7.10
## Max. :119173 Max. :1.29e+09 Max. :27.20 Max. :28.20
##
## Income.composition.of.resources Schooling
## Min. :0.000 Min. : 4.2
## 1st Qu.:0.509 1st Qu.:10.3
## Median :0.673 Median :12.3
## Mean :0.632 Mean :12.1
## 3rd Qu.:0.751 3rd Qu.:14.0
## Max. :0.936 Max. :20.7
## Looking at the summary data we can already see some inconsistencies. In Infant Deaths we see that the max value listed is 1600 which doesn’t make sense since we’re working with per 1000 population data. The same or similar numbers we can see for Infant deaths, Measles, Under five deaths
boxplot(data$Adult.Mortality)
kable(t(head(data[data$Adult.Mortality > boxplot(data$Adult.Mortality)$stats[5], ])))
| 346 | 347 | 348 | 349 | 350 | 351 | |
|---|---|---|---|---|---|---|
| Country | Botswana | Botswana | Botswana | Botswana | Botswana | Botswana |
| Year | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 |
| Status | Developing | Developing | Developing | Developing | Developing | Developing |
| Life.expectancy | 54.8 | 51.7 | 48.1 | 46.4 | 46.0 | 46.7 |
| Adult.Mortality | 491 | 566 | 652 | 693 | 699 | 679 |
| infant.deaths | 2 | 2 | 2 | 2 | 2 | 2 |
| Alcohol | 6.45 | 6.37 | 4.90 | 5.51 | 6.41 | 5.48 |
| percentage.expenditure | 76.32 | 629.84 | 469.58 | 299.37 | 6.33 | 306.95 |
| Hepatitis.B | 93 | 92 | 91 | 9 | 88 | 87 |
| Measles | 6 | 5 | 1 | 59 | 7 | 1 |
| BMI | 33.2 | 32.7 | 32.2 | 31.6 | 31.1 | 3.5 |
| under.five.deaths | 3 | 3 | 4 | 4 | 4 | 4 |
| Polio | 96 | 96 | 96 | 96 | 97 | 97 |
| Total.expenditure | 4.93 | 5.62 | 5.56 | 4.65 | 6.47 | 5.73 |
| Diphtheria | 96 | 96 | 96 | 96 | 97 | 97 |
| HIV.AIDS | 14.4 | 20.6 | 28.4 | 31.9 | 34.6 | 37.2 |
| GDP | 5374.6 | 5351.3 | 4896.6 | 4163.7 | 355.6 | 3129.0 |
| Population | 1884238 | 1855852 | 182933 | 184339 | 1779953 | 1754935 |
| thinness..1.19.years | 9.6 | 1.0 | 1.5 | 1.9 | 11.4 | 11.8 |
| thinness.5.9.years | 9.4 | 9.9 | 1.4 | 1.8 | 11.3 | 11.8 |
| Income.composition.of.resources | 0.610 | 0.593 | 0.580 | 0.567 | 0.558 | 0.560 |
| Schooling | 11.9 | 11.9 | 11.8 | 11.8 | 11.9 | 11.8 |
boxplot(data$infant.deaths)
boxplot(data$infant.deaths)$stats[5]
## [1] 53kable(t(head(data[data$infant.deaths > 200, ])))| 564 | 565 | 566 | 567 | 568 | 569 | |
|---|---|---|---|---|---|---|
| Country | China | China | China | China | China | China |
| Year | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 |
| Status | Developing | Developing | Developing | Developing | Developing | Developing |
| Life.expectancy | 75.4 | 75.2 | 75.0 | 74.9 | 74.5 | 74.4 |
| Adult.Mortality | 89 | 91 | 92 | 93 | 97 | 96 |
| infant.deaths | 201 | 215 | 231 | 248 | 266 | 285 |
| Alcohol | 5.74 | 5.63 | 5.75 | 4.88 | 4.27 | 3.88 |
| percentage.expenditure | 94.434 | 91.267 | 5.661 | 50.283 | 39.225 | 312.662 |
| Hepatitis.B | 99 | 99 | 99 | 99 | 95 | 92 |
| Measles | 6183 | 9943 | 38159 | 52461 | 131441 | 109023 |
| BMI | 3.0 | 29.0 | 28.1 | 27.3 | 26.5 | 25.7 |
| under.five.deaths | 233 | 251 | 268 | 288 | 308 | 332 |
| Polio | 99 | 99 | 99 | 99 | 99 | 94 |
| Total.expenditure | 5.26 | 5.30 | 4.89 | 5.80 | 4.59 | 4.32 |
| Diphtheria | 99 | 99 | 99 | 99 | 97 | 93 |
| HIV.AIDS | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
| GDP | 6337.9 | 5633.8 | 456.5 | 3838.4 | 3471.2 | 2695.4 |
| Population | 135695 | 134413 | 133775 | 133126 | 1324655 | 1317885 |
| thinness..1.19.years | 3.9 | 4.1 | 4.2 | 4.4 | 4.5 | 4.7 |
| thinness.5.9.years | 3.3 | 3.5 | 3.6 | 3.8 | 4.0 | 4.1 |
| Income.composition.of.resources | 0.703 | 0.700 | 0.691 | 0.682 | 0.672 | 0.659 |
| Schooling | 12.4 | 12.8 | 12.5 | 12.2 | 11.9 | 11.4 |
boxplot(data$Measles)
kable(t(head(data[data$Measles > boxplot(data$Measles)$stats[5], ])))
| 1 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|
| Country | Afghanistan | Afghanistan | Afghanistan | Afghanistan | Afghanistan | Afghanistan |
| Year | 2015 | 2012 | 2011 | 2010 | 2009 | 2008 |
| Status | Developing | Developing | Developing | Developing | Developing | Developing |
| Life.expectancy | 65.0 | 59.5 | 59.2 | 58.8 | 58.6 | 58.1 |
| Adult.Mortality | 263 | 272 | 275 | 279 | 281 | 287 |
| infant.deaths | 62 | 69 | 71 | 74 | 77 | 80 |
| Alcohol | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.03 |
| percentage.expenditure | 71.280 | 78.184 | 7.097 | 79.679 | 56.762 | 25.874 |
| Hepatitis.B | 65 | 67 | 68 | 66 | 63 | 64 |
| Measles | 1154 | 2787 | 3013 | 1989 | 2861 | 1599 |
| BMI | 19.1 | 17.6 | 17.2 | 16.7 | 16.2 | 15.7 |
| under.five.deaths | 83 | 93 | 97 | 102 | 106 | 110 |
| Polio | 6 | 67 | 68 | 66 | 63 | 64 |
| Total.expenditure | 8.16 | 8.52 | 7.87 | 9.20 | 9.42 | 8.33 |
| Diphtheria | 65 | 67 | 68 | 66 | 63 | 64 |
| HIV.AIDS | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
| GDP | 584.26 | 669.96 | 63.54 | 553.33 | 445.89 | 373.36 |
| Population | 33736494 | 3696958 | 2978599 | 2883167 | 284331 | 2729431 |
| thinness..1.19.years | 17.2 | 17.9 | 18.2 | 18.4 | 18.6 | 18.8 |
| thinness.5.9.years | 17.3 | 18.0 | 18.2 | 18.4 | 18.7 | 18.9 |
| Income.composition.of.resources | 0.479 | 0.463 | 0.454 | 0.448 | 0.434 | 0.433 |
| Schooling | 10.1 | 9.8 | 9.5 | 9.2 | 8.9 | 8.7 |
boxplot(data$under.five.deaths)
kable(t(head(data[data$under.five.deaths > boxplot(data$under.five.deaths)$stats[5], ])))
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| Country | Afghanistan | Afghanistan | Afghanistan | Afghanistan | Afghanistan | Afghanistan |
| Year | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 |
| Status | Developing | Developing | Developing | Developing | Developing | Developing |
| Life.expectancy | 65.0 | 59.9 | 59.9 | 59.5 | 59.2 | 58.8 |
| Adult.Mortality | 263 | 271 | 268 | 272 | 275 | 279 |
| infant.deaths | 62 | 64 | 66 | 69 | 71 | 74 |
| Alcohol | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |
| percentage.expenditure | 71.280 | 73.524 | 73.219 | 78.184 | 7.097 | 79.679 |
| Hepatitis.B | 65 | 62 | 64 | 67 | 68 | 66 |
| Measles | 1154 | 492 | 430 | 2787 | 3013 | 1989 |
| BMI | 19.1 | 18.6 | 18.1 | 17.6 | 17.2 | 16.7 |
| under.five.deaths | 83 | 86 | 89 | 93 | 97 | 102 |
| Polio | 6 | 58 | 62 | 67 | 68 | 66 |
| Total.expenditure | 8.16 | 8.18 | 8.13 | 8.52 | 7.87 | 9.20 |
| Diphtheria | 65 | 62 | 64 | 67 | 68 | 66 |
| HIV.AIDS | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
| GDP | 584.26 | 612.70 | 631.74 | 669.96 | 63.54 | 553.33 |
| Population | 33736494 | 327582 | 31731688 | 3696958 | 2978599 | 2883167 |
| thinness..1.19.years | 17.2 | 17.5 | 17.7 | 17.9 | 18.2 | 18.4 |
| thinness.5.9.years | 17.3 | 17.5 | 17.7 | 18.0 | 18.2 | 18.4 |
| Income.composition.of.resources | 0.479 | 0.476 | 0.470 | 0.463 | 0.454 | 0.448 |
| Schooling | 10.1 | 10.0 | 9.9 | 9.8 | 9.5 | 9.2 |
ggplot(gather(data[-c(1, 3)]), aes(value)) +
geom_histogram(bins = 10) +
facet_wrap(~key, scales = 'free_x')
ggplot(data, aes(x = Status, y = Life.expectancy)) + geom_boxplot()
ggplot(data, aes(x = Adult.Mortality, y = Life.expectancy)) + geom_boxplot()## Warning: Continuous x aesthetic -- did you forget aes(group=...)?
This original dataset contains Country variable which we would not use for model building. Therefore, this column is excluded from the following data analysis as well as the records with NA in some of the columns mentioned above. This will reduce the size of the original dataset from 2938 to 1649 rows, which captures majority of the information and allows the speed of modeling to be more efficient.
Below lists the summary and structure of the cleaned dataset.
summary(data)## Country Year Status Life.expectancy
## Afghanistan: 16 Min. :2000 Developed : 242 Min. :44.0
## Albania : 16 1st Qu.:2005 Developing:1407 1st Qu.:64.4
## Armenia : 15 Median :2008 Median :71.7
## Austria : 15 Mean :2008 Mean :69.3
## Belarus : 15 3rd Qu.:2011 3rd Qu.:75.0
## Belgium : 15 Max. :2015 Max. :89.0
## (Other) :1557
## Adult.Mortality infant.deaths Alcohol percentage.expenditure
## Min. : 1 Min. : 0.0 Min. : 0.01 Min. : 0
## 1st Qu.: 77 1st Qu.: 1.0 1st Qu.: 0.81 1st Qu.: 37
## Median :148 Median : 3.0 Median : 3.79 Median : 145
## Mean :168 Mean : 32.6 Mean : 4.53 Mean : 699
## 3rd Qu.:227 3rd Qu.: 22.0 3rd Qu.: 7.34 3rd Qu.: 509
## Max. :723 Max. :1600.0 Max. :17.87 Max. :18961
##
## Hepatitis.B Measles BMI under.five.deaths
## Min. : 2.0 Min. : 0 Min. : 2.0 Min. : 0.0
## 1st Qu.:74.0 1st Qu.: 0 1st Qu.:19.5 1st Qu.: 1.0
## Median :89.0 Median : 15 Median :43.7 Median : 4.0
## Mean :79.2 Mean : 2224 Mean :38.1 Mean : 44.2
## 3rd Qu.:96.0 3rd Qu.: 373 3rd Qu.:55.8 3rd Qu.: 29.0
## Max. :99.0 Max. :131441 Max. :77.1 Max. :2100.0
##
## Polio Total.expenditure Diphtheria HIV.AIDS
## Min. : 3.0 Min. : 0.74 Min. : 2.0 Min. : 0.10
## 1st Qu.:81.0 1st Qu.: 4.41 1st Qu.:82.0 1st Qu.: 0.10
## Median :93.0 Median : 5.84 Median :92.0 Median : 0.10
## Mean :83.6 Mean : 5.96 Mean :84.2 Mean : 1.98
## 3rd Qu.:97.0 3rd Qu.: 7.47 3rd Qu.:97.0 3rd Qu.: 0.70
## Max. :99.0 Max. :14.39 Max. :99.0 Max. :50.60
##
## GDP Population thinness..1.19.years thinness.5.9.years
## Min. : 2 Min. :3.40e+01 Min. : 0.10 Min. : 0.10
## 1st Qu.: 462 1st Qu.:1.92e+05 1st Qu.: 1.60 1st Qu.: 1.70
## Median : 1593 Median :1.42e+06 Median : 3.00 Median : 3.20
## Mean : 5566 Mean :1.47e+07 Mean : 4.85 Mean : 4.91
## 3rd Qu.: 4719 3rd Qu.:7.66e+06 3rd Qu.: 7.10 3rd Qu.: 7.10
## Max. :119173 Max. :1.29e+09 Max. :27.20 Max. :28.20
##
## Income.composition.of.resources Schooling
## Min. :0.000 Min. : 4.2
## 1st Qu.:0.509 1st Qu.:10.3
## Median :0.673 Median :12.3
## Mean :0.632 Mean :12.1
## 3rd Qu.:0.751 3rd Qu.:14.0
## Max. :0.936 Max. :20.7
## data = na.omit(data)
data = data[-1] #exclude country from dataset
str(data)## 'data.frame': 1649 obs. of 21 variables:
## $ Year : int 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 ...
## $ Status : Factor w/ 2 levels "Developed","Developing": 2 2 2 2 2 2 2 2 2 2 ...
## $ Life.expectancy : num 65 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 ...
## $ Adult.Mortality : int 263 271 268 272 275 279 281 287 295 295 ...
## $ infant.deaths : int 62 64 66 69 71 74 77 80 82 84 ...
## $ Alcohol : num 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.02 0.03 ...
## $ percentage.expenditure : num 71.3 73.5 73.2 78.2 7.1 ...
## $ Hepatitis.B : int 65 62 64 67 68 66 63 64 63 64 ...
## $ Measles : int 1154 492 430 2787 3013 1989 2861 1599 1141 1990 ...
## $ BMI : num 19.1 18.6 18.1 17.6 17.2 16.7 16.2 15.7 15.2 14.7 ...
## $ under.five.deaths : int 83 86 89 93 97 102 106 110 113 116 ...
## $ Polio : int 6 58 62 67 68 66 63 64 63 58 ...
## $ Total.expenditure : num 8.16 8.18 8.13 8.52 7.87 9.2 9.42 8.33 6.73 7.43 ...
## $ Diphtheria : int 65 62 64 67 68 66 63 64 63 58 ...
## $ HIV.AIDS : num 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...
## $ GDP : num 584.3 612.7 631.7 670 63.5 ...
## $ Population : num 33736494 327582 31731688 3696958 2978599 ...
## $ thinness..1.19.years : num 17.2 17.5 17.7 17.9 18.2 18.4 18.6 18.8 19 19.2 ...
## $ thinness.5.9.years : num 17.3 17.5 17.7 18 18.2 18.4 18.7 18.9 19.1 19.3 ...
## $ Income.composition.of.resources: num 0.479 0.476 0.47 0.463 0.454 0.448 0.434 0.433 0.415 0.405 ...
## $ Schooling : num 10.1 10 9.9 9.8 9.5 9.2 8.9 8.7 8.4 8.1 ...Data Visualization
Let’s take a look of the dataset using plots of Life Expectancy vs Status or Year. The boxplot indicates that there is significant difference in Life Expectancy between the Developed and Developing countries. As expected, the Life Expectancy increases as the Year passes by and the Violin plot shows that the data is well distributed across different years.
par(mfrow=c(1,2))
# Histogram of Life Expectancy
hist(data$Life.expectancy,
xlab = "Life Expectancy",
main = "Distribution of Life Expectancy",
col = "dodgerblue",
breaks = 25)
# Boxplot of Life Expectancy vs Country Status (Developed vs Developing)
plot(data$Status,
data$Life.expectancy,
xlab = "Status",
ylab = "Life Expectancy",
main = "Life Expectancy vs. Status",
col = c(2,3))
# Violin plot of Life Expectancy vs. Year
data %>% ggplot() + geom_violin(aes(x=Year, y=Life.expectancy, group=Year, fill=Year)) + labs(title = "Life Expectancy vs. Year")
Colinearity
Colinearity issue is visualized using the following plots. Resulsts show that some predictors have strong collinearity issues, such as infant.deaths vs. under.five.deaths, GDP vs. percentage.expenditure, Population vs. thinness..1.19.years etc.
corrplot(cor(data[-c(2)]), method = "circle")
ggpairs(data[-c(2)])
round(cor(data[-c(2)]),2)## Year Life.expectancy Adult.Mortality
## Year 1.00 0.05 -0.04
## Life.expectancy 0.05 1.00 -0.70
## Adult.Mortality -0.04 -0.70 1.00
## infant.deaths 0.01 -0.17 0.04
## Alcohol -0.11 0.40 -0.18
## percentage.expenditure 0.07 0.41 -0.24
## Hepatitis.B 0.11 0.20 -0.11
## Measles -0.05 -0.07 0.00
## BMI 0.01 0.54 -0.35
## under.five.deaths 0.01 -0.19 0.06
## Polio -0.02 0.33 -0.20
## Total.expenditure 0.06 0.17 -0.09
## Diphtheria 0.03 0.34 -0.19
## HIV.AIDS -0.12 -0.59 0.55
## GDP 0.10 0.44 -0.26
## Population 0.01 -0.02 -0.02
## thinness..1.19.years 0.02 -0.46 0.27
## thinness.5.9.years 0.01 -0.46 0.29
## Income.composition.of.resources 0.12 0.72 -0.44
## Schooling 0.09 0.73 -0.42
## infant.deaths Alcohol percentage.expenditure
## Year 0.01 -0.11 0.07
## Life.expectancy -0.17 0.40 0.41
## Adult.Mortality 0.04 -0.18 -0.24
## infant.deaths 1.00 -0.11 -0.09
## Alcohol -0.11 1.00 0.42
## percentage.expenditure -0.09 0.42 1.00
## Hepatitis.B -0.23 0.11 0.02
## Measles 0.53 -0.05 -0.06
## BMI -0.23 0.35 0.24
## under.five.deaths 1.00 -0.10 -0.09
## Polio -0.16 0.24 0.13
## Total.expenditure -0.15 0.21 0.18
## Diphtheria -0.16 0.24 0.13
## HIV.AIDS 0.01 -0.03 -0.10
## GDP -0.10 0.44 0.96
## Population 0.67 -0.03 -0.02
## thinness..1.19.years 0.46 -0.40 -0.26
## thinness.5.9.years 0.46 -0.39 -0.26
## Income.composition.of.resources -0.13 0.56 0.40
## Schooling -0.21 0.62 0.42
## Hepatitis.B Measles BMI under.five.deaths
## Year 0.11 -0.05 0.01 0.01
## Life.expectancy 0.20 -0.07 0.54 -0.19
## Adult.Mortality -0.11 0.00 -0.35 0.06
## infant.deaths -0.23 0.53 -0.23 1.00
## Alcohol 0.11 -0.05 0.35 -0.10
## percentage.expenditure 0.02 -0.06 0.24 -0.09
## Hepatitis.B 1.00 -0.12 0.14 -0.24
## Measles -0.12 1.00 -0.15 0.52
## BMI 0.14 -0.15 1.00 -0.24
## under.five.deaths -0.24 0.52 -0.24 1.00
## Polio 0.46 -0.06 0.19 -0.17
## Total.expenditure 0.11 -0.11 0.19 -0.15
## Diphtheria 0.59 -0.06 0.18 -0.18
## HIV.AIDS -0.09 0.00 -0.21 0.02
## GDP 0.04 -0.06 0.27 -0.10
## Population -0.13 0.32 -0.08 0.66
## thinness..1.19.years -0.13 0.18 -0.55 0.46
## thinness.5.9.years -0.13 0.17 -0.55 0.46
## Income.composition.of.resources 0.18 -0.06 0.51 -0.15
## Schooling 0.22 -0.12 0.55 -0.23
## Polio Total.expenditure Diphtheria HIV.AIDS
## Year -0.02 0.06 0.03 -0.12
## Life.expectancy 0.33 0.17 0.34 -0.59
## Adult.Mortality -0.20 -0.09 -0.19 0.55
## infant.deaths -0.16 -0.15 -0.16 0.01
## Alcohol 0.24 0.21 0.24 -0.03
## percentage.expenditure 0.13 0.18 0.13 -0.10
## Hepatitis.B 0.46 0.11 0.59 -0.09
## Measles -0.06 -0.11 -0.06 0.00
## BMI 0.19 0.19 0.18 -0.21
## under.five.deaths -0.17 -0.15 -0.18 0.02
## Polio 1.00 0.12 0.61 -0.11
## Total.expenditure 0.12 1.00 0.13 0.04
## Diphtheria 0.61 0.13 1.00 -0.12
## HIV.AIDS -0.11 0.04 -0.12 1.00
## GDP 0.16 0.18 0.16 -0.11
## Population -0.05 -0.08 -0.04 -0.03
## thinness..1.19.years -0.16 -0.21 -0.19 0.17
## thinness.5.9.years -0.17 -0.22 -0.18 0.18
## Income.composition.of.resources 0.31 0.18 0.34 -0.25
## Schooling 0.35 0.24 0.35 -0.21
## GDP Population thinness..1.19.years
## Year 0.10 0.01 0.02
## Life.expectancy 0.44 -0.02 -0.46
## Adult.Mortality -0.26 -0.02 0.27
## infant.deaths -0.10 0.67 0.46
## Alcohol 0.44 -0.03 -0.40
## percentage.expenditure 0.96 -0.02 -0.26
## Hepatitis.B 0.04 -0.13 -0.13
## Measles -0.06 0.32 0.18
## BMI 0.27 -0.08 -0.55
## under.five.deaths -0.10 0.66 0.46
## Polio 0.16 -0.05 -0.16
## Total.expenditure 0.18 -0.08 -0.21
## Diphtheria 0.16 -0.04 -0.19
## HIV.AIDS -0.11 -0.03 0.17
## GDP 1.00 -0.02 -0.28
## Population -0.02 1.00 0.28
## thinness..1.19.years -0.28 0.28 1.00
## thinness.5.9.years -0.28 0.28 0.93
## Income.composition.of.resources 0.45 -0.01 -0.45
## Schooling 0.47 -0.04 -0.49
## thinness.5.9.years
## Year 0.01
## Life.expectancy -0.46
## Adult.Mortality 0.29
## infant.deaths 0.46
## Alcohol -0.39
## percentage.expenditure -0.26
## Hepatitis.B -0.13
## Measles 0.17
## BMI -0.55
## under.five.deaths 0.46
## Polio -0.17
## Total.expenditure -0.22
## Diphtheria -0.18
## HIV.AIDS 0.18
## GDP -0.28
## Population 0.28
## thinness..1.19.years 0.93
## thinness.5.9.years 1.00
## Income.composition.of.resources -0.44
## Schooling -0.47
## Income.composition.of.resources Schooling
## Year 0.12 0.09
## Life.expectancy 0.72 0.73
## Adult.Mortality -0.44 -0.42
## infant.deaths -0.13 -0.21
## Alcohol 0.56 0.62
## percentage.expenditure 0.40 0.42
## Hepatitis.B 0.18 0.22
## Measles -0.06 -0.12
## BMI 0.51 0.55
## under.five.deaths -0.15 -0.23
## Polio 0.31 0.35
## Total.expenditure 0.18 0.24
## Diphtheria 0.34 0.35
## HIV.AIDS -0.25 -0.21
## GDP 0.45 0.47
## Population -0.01 -0.04
## thinness..1.19.years -0.45 -0.49
## thinness.5.9.years -0.44 -0.47
## Income.composition.of.resources 1.00 0.78
## Schooling 0.78 1.00# train test split 70/30 hold out
train_size = floor(0.7 * nrow(data))
train_idx = sample(nrow(data), train_size)
data.train = data[train_idx, ]
data.test = data[-train_idx, ]
model.additive = lm(Life.expectancy ~ ., data.train)
cv.lm(data.train, model.additive, m = 5, plotit = FALSE)## Analysis of Variance Table
##
## Response: Life.expectancy
## Df Sum Sq Mean Sq F value Pr(>F)
## Year 1 417 417 33.63 8.6e-09 ***
## Status 1 17517 17517 1411.46 < 2e-16 ***
## Adult.Mortality 1 28083 28083 2262.80 < 2e-16 ***
## infant.deaths 1 1105 1105 89.04 < 2e-16 ***
## Alcohol 1 2219 2219 178.78 < 2e-16 ***
## percentage.expenditure 1 1108 1108 89.29 < 2e-16 ***
## Hepatitis.B 1 814 814 65.58 1.4e-15 ***
## Measles 1 16 16 1.27 0.2602
## BMI 1 3647 3647 293.86 < 2e-16 ***
## under.five.deaths 1 2628 2628 211.79 < 2e-16 ***
## Polio 1 791 791 63.74 3.5e-15 ***
## Total.expenditure 1 13 13 1.06 0.3023
## Diphtheria 1 405 405 32.59 1.4e-08 ***
## HIV.AIDS 1 6607 6607 532.33 < 2e-16 ***
## GDP 1 209 209 16.83 4.4e-05 ***
## Population 1 24 24 1.90 0.1683
## thinness..1.19.years 1 121 121 9.75 0.0018 **
## thinness.5.9.years 1 29 29 2.32 0.1279
## Income.composition.of.resources 1 4467 4467 359.93 < 2e-16 ***
## Schooling 1 1997 1997 160.92 < 2e-16 ***
## Residuals 1133 14061 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## fold 1
## Observations in test set: 230
## 2275 2699 2124 834 2276 2697 884 1289 2160 1354
## Predicted 73.700 68.50 75.89 70.28 73.581 71.27 60.77 80.46 61.10 72.48
## cvpred 73.897 68.54 75.68 70.38 73.758 71.28 60.66 80.41 61.08 72.55
## Life.expectancy 73.600 66.00 74.30 69.00 73.000 74.00 64.20 81.60 59.60 66.60
## CV residual -0.297 -2.54 -1.38 -1.38 -0.758 2.72 3.54 1.19 -1.48 -5.95
## 1727 1140 1295 1590 508 1629 1366 2043 2258 688
## Predicted 69.21 68.40 80.310 72.45 79.657 60.47 63.4 76.5 63.58 75.52
## cvpred 69.25 68.49 80.227 72.53 79.887 60.42 63.4 76.5 63.82 75.39
## Life.expectancy 64.50 74.50 79.900 74.50 80.000 53.60 62.1 76.8 62.10 78.20
## CV residual -4.75 6.01 -0.327 1.97 0.113 -6.82 -1.3 0.3 -1.72 2.81
## 2709 2694 2855 1337 1348 824 283 392 1110 1721
## Predicted 60.68 71.991 62.56 73.496 75.80 71.337 59.42 74.35 70.25 72.47
## cvpred 60.23 72.081 62.17 73.655 75.91 71.447 59.38 74.25 70.34 72.53
## Life.expectancy 63.50 71.600 69.40 73.300 69.90 72.000 56.50 72.90 65.80 67.30
## CV residual 3.27 -0.481 7.23 -0.355 -6.01 0.553 -2.88 -1.35 -4.54 -5.23
## 277 1979 299 92 1826 1002 1193 779 2206 2064
## Predicted 62.8 64.33 59.47 79.1 67.63 83.36 69.05 69.11 72.107 77.22
## cvpred 62.7 64.32 58.97 79.2 67.44 83.09 69.46 69.16 72.238 77.16
## Life.expectancy 59.1 62.20 65.00 74.7 64.30 79.90 66.00 72.90 72.600 78.70
## CV residual -3.6 -2.12 6.03 -4.5 -3.14 -3.19 -3.46 3.74 0.362 1.54
## 1493 2257 118 265 361 1963 1772 388 2852 634
## Predicted 63.37 61.33 86.4 70.92 73.824 74.12 58.97 75.05 68.35 73.70
## cvpred 63.36 61.25 86.4 71.01 74.032 74.32 58.99 74.94 68.35 73.89
## Life.expectancy 61.10 62.80 81.9 69.60 73.300 77.20 53.20 73.90 71.00 78.90
## CV residual -2.26 1.55 -4.5 -1.41 -0.732 2.88 -5.79 -1.04 2.65 5.01
## 1674 2928 2572 602 1682 300 203 474 826 2144
## Predicted 71.825 52.3495 71.71 64.2 70.651 58.10 64.26 62.96 71.769 71.0
## cvpred 71.867 52.3136 71.72 64.1 70.656 57.51 64.73 62.84 71.851 71.1
## Life.expectancy 72.800 52.4000 74.50 63.0 71.500 64.20 67.80 64.10 71.700 67.3
## CV residual 0.933 0.0864 2.78 -1.1 0.844 6.69 3.07 1.26 -0.151 -3.8
## 1966 1288 1723 2817 796 204 83 230 2931 2029
## Predicted 73.00 82.9 71.17 75.03 72.42 65.25 77.50 72.91735 54.55 68.104
## cvpred 73.18 82.9 71.22 75.16 72.52 65.19 77.67 73.00934 54.63 67.735
## Life.expectancy 76.80 81.8 66.90 76.60 74.40 67.30 76.00 73.00000 46.60 67.900
## CV residual 3.62 -1.1 -4.32 1.44 1.88 2.11 -1.67 -0.00934 -8.03 0.165
## 147 1022 1768 2725 427 2829 2002 293 547 2228
## Predicted 70.54 63.16 62.13 55.37 54.95 70.62 70.88 67.32 77.2 64.754
## cvpred 70.68 63.23 62.15 55.44 54.88 70.72 70.96 67.19 77.3 64.591
## Life.expectancy 72.20 58.30 54.80 53.20 53.40 69.10 72.10 68.30 81.0 64.300
## CV residual 1.52 -4.93 -7.35 -2.24 -1.48 -1.62 1.14 1.11 3.7 -0.291
## 1618 134 1967 1615 1997 2737 1970 1216 8 1532
## Predicted 70.025 81.03 72.96 70.61 71.17 72.36 72.19 66.59 61.72 75.759
## cvpred 70.017 81.04 73.12 70.57 71.33 72.51 72.31 66.55 61.67 75.586
## Life.expectancy 69.600 84.00 76.50 72.70 73.20 69.20 75.80 66.70 58.10 76.000
## CV residual -0.417 2.96 3.38 2.13 1.87 -3.31 3.49 0.15 -3.57 0.414
## 1336 421 1777 862 235 2033 394 1465 1150 2692
## Predicted 74.55 61.47 50.148 53.74 72.15 68.152 72.650 74.004 68.57 70.46
## cvpred 74.75 61.39 50.004 53.31 72.25 67.836 72.447 74.177 68.66 70.56
## Life.expectancy 73.40 57.40 51.000 59.10 68.10 67.300 72.200 74.700 72.20 72.40
## CV residual -1.35 -3.99 0.996 5.79 -4.15 -0.536 -0.247 0.523 3.54 1.84
## 2733 908 1191 133 279 592 18 272 2679 886
## Predicted 71.177 72.73 61.96 80.70 61.70 70.930 75.68 69.45 75.27 59.3
## cvpred 71.271 72.79 62.35 80.46 61.53 71.024 75.84 69.44 75.33 59.2
## Life.expectancy 71.000 68.50 66.80 88.00 58.40 71.400 77.50 68.30 73.50 63.3
## CV residual -0.271 -4.29 4.45 7.54 -3.13 0.376 1.66 -1.14 -1.83 4.1
## 462 909 864 1534 2291 681 1242 87 2585 1952
## Predicted 69.15 72.68 51.58 78.19 70.26 76.33 69.053 77.32 68.43 64.1776
## cvpred 69.12 72.74 51.27 77.93 70.23 76.26 69.099 77.51 68.35 64.2184
## Life.expectancy 77.00 68.30 58.50 71.60 72.20 79.10 69.300 75.60 71.10 64.2000
## CV residual 7.88 -4.44 7.23 -6.33 1.97 2.84 0.201 -1.91 2.75 -0.0184
## 833 567 1531 1541 2133 1125 126 872 1544 2059
## Predicted 70.5 73.98 79.43 82.134 72.32 63.352 83.49 76.162 77.47 78.04
## cvpred 70.6 73.98 79.29 82.142 72.08 63.387 83.44 76.334 77.43 78.01
## Life.expectancy 68.9 74.90 72.00 81.400 77.00 62.700 79.90 75.600 86.00 83.00
## CV residual -1.7 0.92 -7.29 -0.742 4.92 -0.687 -3.54 -0.734 8.57 4.99
## 795 2658 359 1 2149 36 2910 1642 2850 2812
## Predicted 74.361 70.032 74.05 62.79 70.33 74.8984 61.83 78.31 68.5 76.002
## cvpred 74.485 70.021 74.15 62.67 70.43 75.0195 61.73 78.29 68.5 76.333
## Life.expectancy 74.700 69.700 73.60 65.00 64.80 75.1000 59.20 80.00 75.0 76.800
## CV residual 0.215 -0.321 -0.55 2.33 -5.63 0.0805 -2.53 1.71 6.5 0.467
## 1832 2155 2577 1626 237 1627 1237 458 1393 1497
## Predicted 83.65 65.239 71.0 57.1 69.52 57.61 70.73 69.55 64.022 63.07
## cvpred 84.04 65.218 70.9 57.0 69.68 57.57 70.82 69.52 63.787 63.17
## Life.expectancy 81.40 64.600 73.5 55.5 67.70 55.00 69.50 72.10 64.300 59.20
## CV residual -2.64 -0.618 2.6 -1.5 -1.98 -2.57 -1.32 2.58 0.513 -3.97
## 470 1189 2025 507 1207 14 1551 1895 536 266
## Predicted 66.161 67.958 67.71 81.642 70.39 62.24 81.23 52.20 51.94 70.67
## cvpred 66.081 68.375 67.18 81.924 70.36 62.84 81.18 52.19 51.77 70.73
## Life.expectancy 66.600 67.600 68.40 81.000 68.30 56.20 78.60 53.60 49.60 69.40
## CV residual 0.519 -0.775 1.22 -0.924 -2.06 -6.64 -2.58 1.41 -2.17 -1.33
## 2395 364 2638 2475 22 2619 350 367 2702 2856
## Predicted 65.3 76.65 75.98 71.013 72.76 64.85 45.073 74.87 68.3 61.15
## cvpred 65.4 76.72 76.11 71.139 72.88 64.75 45.265 75.04 68.3 60.82
## Life.expectancy 62.0 72.00 72.90 71.400 76.20 59.70 46.000 71.00 65.6 69.30
## CV residual -3.4 -4.72 -3.21 0.261 3.32 -5.05 0.735 -4.04 -2.7 8.48
## 1819 1616 550 301 244 2558 352 110 138 2128
## Predicted 66.72 70.42 74.45 58.68 78.13 69.11 43.98 70.89 76.30 74.84
## cvpred 66.63 70.36 74.58 58.18 77.92 69.16 44.17 70.97 76.05 74.64
## Life.expectancy 68.00 71.80 79.10 63.30 83.00 68.10 47.80 72.60 79.80 72.90
## CV residual 1.37 1.44 4.52 5.12 5.08 -1.06 3.63 1.63 3.75 -1.74
## 1565 2494 1631 1000 2640 2031 39 1287 1833
## Predicted 62.49 55.606 55.49 83.00 74.24 68.687 73.427 82.908 81.258
## cvpred 62.33 55.688 55.45 82.98 74.35 68.407 73.535 82.863 81.584
## Life.expectancy 69.00 55.000 52.00 81.00 72.50 67.500 74.400 82.000 81.100
## CV residual 6.67 -0.688 -3.45 -1.98 -1.85 -0.907 0.865 -0.863 -0.484
## 597 137 1582 2652 2606 2832 1141 2165 387
## Predicted 65.34 80.946 47.16 71.049 68.072 69.123 72.09 53.80 76.65
## cvpred 65.28 80.699 47.23 71.173 67.913 69.149 72.24 53.63 76.61
## Life.expectancy 62.20 81.000 45.10 71.000 67.200 68.300 74.30 57.00 74.10
## CV residual -3.08 0.301 -2.13 -0.173 -0.713 -0.849 2.06 3.37 -2.51
## 2401 2555 911 13 1274 37 472 2145 786 2001
## Predicted 53.963 69.339 75.15 58.81 79.22 74.418 66.065 75.33 69.65 70.77
## cvpred 54.457 69.409 75.21 58.75 79.69 74.516 65.958 75.43 69.72 70.84
## Life.expectancy 55.300 69.600 68.00 56.70 81.00 74.900 65.600 66.40 72.00 72.30
## CV residual 0.843 0.191 -7.21 -2.05 1.31 0.384 -0.358 -9.03 2.28 1.46
## 2657 2603 632 901 2402 1290 2367 1646 489 2834
## Predicted 69.345 68.817 73.26 73.83 52.44 79.61 65.0 77.60 55.95 70.36
## cvpred 69.548 68.382 73.41 73.92 52.59 79.53 65.2 77.54 55.91 70.43
## Life.expectancy 69.900 68.000 79.20 69.60 54.50 81.50 68.3 78.70 53.60 67.90
## CV residual 0.352 -0.382 5.79 -4.32 1.91 1.97 3.1 1.16 -2.31 -2.53
## 2289 2840 197 2013 1015 1018 1689 243 531 12
## Predicted 71.527 70.02 68.17 74.349 65.12 63.509 71.85 77.94 55.0 58.18
## cvpred 71.557 70.06 67.96 74.442 65.09 63.486 71.91 77.74 54.9 58.11
## Life.expectancy 72.200 67.10 73.00 73.700 61.20 63.000 75.60 87.00 52.2 57.00
## CV residual 0.643 -2.96 5.04 -0.742 -3.89 -0.486 3.69 9.26 -2.7 -1.11
## 1614 2204
## Predicted 72.478 72.459
## cvpred 72.448 72.602
## Life.expectancy 73.400 73.200
## CV residual 0.952 0.598
##
## Sum of squares = 2534 Mean square = 11 n = 230
##
## fold 2
## Observations in test set: 231
## 1108 2718 1609 2297 2933 2015 2405 2429 1677 605
## Predicted 66.501 60.07 71.21 64.03 41.71 70.99 51.02 81.819 72.16 57.57
## cvpred 66.421 60.07 71.01 62.68 41.89 71.21 50.88 81.648 72.17 56.96
## Life.expectancy 66.000 60.00 76.30 71.80 44.60 73.90 53.70 82.000 71.80 59.60
## CV residual -0.421 -0.07 5.29 9.12 2.71 2.69 2.82 0.352 -0.37 2.64
## 2447 1740 1243 139 146 1696 1673 2736 2163 1718
## Predicted 71.79 74.895 67.83 79.035 72.568 73.36 71.62 72.12 55.68 72.90
## cvpred 71.79 74.814 68.05 79.026 72.665 73.32 71.82 72.05 55.47 73.01
## Life.expectancy 74.50 74.600 65.90 79.400 72.500 75.00 73.30 69.80 53.40 68.40
## CV residual 2.71 -0.214 -2.15 0.374 -0.165 1.68 1.48 -2.25 -2.07 -4.61
## 2365 2434 466 242 1690 468 1281 777 1962 2707
## Predicted 66.65 79 67.3 80.7 75.191 66.555 78.393 71.25 72.13 61.35
## cvpred 66.59 79 67.2 80.6 75.068 66.506 78.525 71.31 72.23 60.35
## Life.expectancy 68.70 89 68.3 89.0 75.700 67.400 79.300 73.60 77.50 63.70
## CV residual 2.11 10 1.1 8.4 0.632 0.894 0.775 2.29 5.27 3.35
## 43 583 1530 1358 461 1114 1462 1154 1904 1094
## Predicted 71.821 74.24 76.7 70.7 68.84 66.493 74.08 67.73 50.45 60.16
## cvpred 71.973 74.11 76.6 70.8 68.73 66.515 74.01 67.69 49.69 60.07
## Life.expectancy 72.900 73.60 71.1 64.7 71.10 66.300 75.00 71.00 49.20 57.60
## CV residual 0.927 -0.51 -5.5 -6.1 2.37 -0.215 0.99 3.31 -0.49 -2.47
## 1357 1903 1686 534 2222 1974 989 1756 1255 2061
## Predicted 71.39 44.69 74.55 53.92 66.198 73.36 72.19 69.90 84.897 78.13
## cvpred 71.54 43.77 74.56 53.94 66.055 73.34 72.19 69.82 84.472 78.07
## Life.expectancy 64.60 49.80 76.60 51.20 66.600 75.50 73.90 71.80 84.000 79.60
## CV residual -6.94 6.03 2.04 -2.74 0.545 2.16 1.71 1.98 -0.472 1.53
## 1754 276 2296 345 1947 1239 1643 264 1280 263
## Predicted 71.9 61.32 71.172 59.48 65.960 68.85 78.19 71.03 77.65 71.05
## cvpred 71.7 61.43 71.172 59.53 66.357 68.94 78.18 70.98 77.71 70.98
## Life.expectancy 72.8 59.30 72.000 56.90 65.500 77.00 79.60 69.60 79.30 69.50
## CV residual 1.1 -2.13 0.828 -2.63 -0.857 8.06 1.42 -1.38 1.59 -1.48
## 793 2445 2663 1244 1593 2065 1456 256 1527 2509
## Predicted 71.29 71.60 70.32 67.41 72.48 78.41 75.24 82.88 77.97 84.34
## cvpred 71.49 71.64 70.53 67.67 72.61 78.19 75.33 82.95 77.97 84.25
## Life.expectancy 75.10 74.50 69.20 64.70 74.00 78.50 73.00 77.60 72.80 81.70
## CV residual 3.61 2.86 -1.33 -2.97 1.39 0.31 -2.33 -5.35 -5.17 -2.55
## 2284 1212 252 1605 902 1083 1793 1210 2123 130
## Predicted 72.8597 69.2 84.09 72.90 72.09 62.47 62.577 69.81 75.93 81.997
## cvpred 72.9713 69.7 83.83 72.69 72.34 62.23 62.659 70.33 75.99 81.671
## Life.expectancy 72.9000 67.3 78.80 77.90 69.40 56.40 63.200 67.70 74.40 81.400
## CV residual -0.0713 -2.4 -5.03 5.21 -2.94 -5.83 0.541 -2.63 -1.59 -0.271
## 1610 1338 282 1476 2443 1351 27 932 1538 1973
## Predicted 71.00 73.410 61.31 56.02 71.91 72.69 72.595 80.7 77.66 73.48
## cvpred 70.83 73.614 61.25 56.28 71.96 72.63 72.529 80.3 77.56 73.39
## Life.expectancy 75.90 73.100 56.80 52.10 74.70 68.50 73.500 82.2 71.60 75.70
## CV residual 5.07 -0.514 -4.45 -4.18 2.74 -4.13 0.971 1.9 -5.96 2.31
## 868 933 589 1120 1464 686 390 119 2406 2831
## Predicted 78.67 80.85 73.52 66.89 74.453 76.13 74.60 85.42 51.15 70.32
## cvpred 78.73 80.44 73.43 66.81 74.395 76.27 74.68 85.19 51.02 70.37
## Life.expectancy 77.30 82.00 72.40 65.30 74.900 78.50 73.40 81.70 54.00 68.50
## CV residual -1.43 1.56 -1.03 -1.51 0.505 2.23 -1.28 -3.49 2.98 -1.87
## 953 878 1064 518 863 568 1213 2225 935 949
## Predicted 67.17 74.67 68.50 52.29 53.43 73.49 71.90 66.052 76.36 66.00
## cvpred 67.03 74.62 68.52 52.49 52.83 74.23 72.25 65.918 76.51 65.91
## Life.expectancy 61.70 72.30 77.00 49.20 58.80 74.50 67.20 65.400 81.70 64.60
## CV residual -5.33 -2.32 8.48 -3.29 5.97 0.27 -5.05 -0.518 5.19 -1.31
## 994 2624 857 1217 1284 2269 40 302 2689 501 2294
## Predicted 63.57 60.76 57.99 68.7 81.38 73.95 72.6 58.54 71.63 77.83 70.96
## cvpred 62.51 60.75 58.07 68.9 81.25 73.72 72.7 57.51 71.86 78.09 70.92
## Life.expectancy 71.80 56.70 61.40 66.5 82.50 74.90 74.1 62.50 73.50 81.50 72.10
## CV residual 9.29 -4.05 3.33 -2.4 1.25 1.18 1.4 4.99 1.64 3.41 1.18
## 1573 1469 891 2499 2366 2207 1286 1872 1471 2695
## Predicted 59.04 67.34 57.99 40.15 66.56 71.29 82.711 68.88 70.1 71.695
## cvpred 59.16 66.11 57.58 40.35 66.46 71.42 82.554 68.85 68.6 71.791
## Life.expectancy 56.70 73.90 58.50 47.80 68.50 76.00 82.000 71.20 73.5 71.200
## CV residual -2.46 7.79 0.92 7.45 2.04 4.58 -0.554 2.35 4.9 -0.591
## 2909 2580 2563 2230 2550 1662 2607 1524 260 1385
## Predicted 63.264 69.79 68.28 65.67 69.58 62.1 68.22 76.81 70.58 73.53
## cvpred 63.332 69.82 68.35 65.43 69.57 62.2 68.33 76.66 70.52 73.17
## Life.expectancy 63.000 72.50 65.90 63.40 73.00 66.0 66.90 73.40 69.40 65.20
## CV residual -0.332 2.68 -2.45 -2.03 3.43 3.8 -1.43 -3.26 -1.12 -7.97
## 836 1981 759 2408 2644 1472 2370 2823 2686 2915
## Predicted 63.74 63.69 59.39 54.20 76.61 69.63 67.708 75.851 74.948 53.89
## cvpred 64.01 63.78 59.39 54.16 76.48 68.24 67.705 75.762 74.861 54.23
## Life.expectancy 57.90 61.80 61.30 56.00 72.30 73.20 67.600 75.400 74.500 52.60
## CV residual -6.11 -1.98 1.91 1.84 -4.18 4.96 -0.105 -0.362 -0.361 -1.63
## 2047 2156 1245 912 1977 1352 2407 2656 344 112
## Predicted 77.80 63.435 71.0 75.19 64.42 72.31 51.6 69.18 60.02 71.528
## cvpred 77.77 63.094 71.1 75.12 64.53 72.39 51.5 69.48 60.08 71.582
## Life.expectancy 75.50 63.800 66.8 67.90 62.70 67.80 54.9 71.00 57.50 72.000
## CV residual -2.27 0.706 -4.3 -7.22 -1.83 -4.59 3.4 1.52 -2.58 0.418
## 640 2565 985 239 2272 1063 2034 285 460 2853
## Predicted 75.03 68.43 71.75 71.3 73.844 68.22 67.786 60.37 70.58 62.76
## cvpred 75.09 68.49 71.89 71.1 73.606 68.27 67.951 60.31 70.33 61.85
## Life.expectancy 77.50 65.90 73.20 67.7 74.100 71.10 67.000 55.80 71.40 69.90
## CV residual 2.41 -2.59 1.31 -3.4 0.494 2.83 -0.951 -4.51 1.07 8.05
## 1029 1870 2273 2676 2822 2051 2427 2058 1373 2932
## Predicted 79.70 69.36 72.54 75.83 77.05 77.20 81.30 77.72 54.696 52.56
## cvpred 79.37 69.28 72.53 75.64 76.83 77.25 81.56 77.77 54.768 52.27
## Life.expectancy 86.00 72.50 74.00 74.20 75.40 74.90 82.60 86.00 54.100 45.40
## CV residual 6.63 3.22 1.47 -1.44 -1.43 -2.35 1.04 8.23 -0.668 -6.87
## 1479 1350 1563 678 1644 155 1549 1698 1097 483
## Predicted 63.7 71.59 63.30 77.70 78.712 70.83 78.328 72.82 58.13 60.86
## cvpred 63.3 71.71 63.31 77.51 78.651 71.01 78.407 72.87 58.13 60.91
## Life.expectancy 52.3 69.10 61.90 79.70 79.300 68.40 78.800 75.00 56.30 56.40
## CV residual -11.0 -2.61 -1.41 2.19 0.649 -2.61 0.393 2.13 -1.83 -4.51
## 1449 675 2641 820 2710 1545 2849 2288 829 2573
## Predicted 77.17 77.61 74.7 71.64 61.48 77.34 68.57 71.220 71.257 70.96
## cvpred 77.16 77.98 74.7 71.61 60.51 77.46 68.68 71.347 71.245 71.07
## Life.expectancy 72.60 83.00 72.6 73.30 63.40 83.00 78.00 72.300 71.000 74.30
## CV residual -4.56 5.02 -2.1 1.69 2.89 5.54 9.32 0.953 -0.245 3.23
## 772 262 791 2917 983 599 1761 2060 573 2635
## Predicted 71.18 70.67 72.59 52.50 72.94 64.79 68.825 78.35 73.501 72.917
## cvpred 71.13 70.62 72.58 52.59 72.76 64.78 68.928 78.29 74.004 73.135
## Life.expectancy 73.60 69.50 75.30 49.30 73.90 61.30 69.900 82.00 73.100 73.300
## CV residual 2.47 -1.12 2.72 -3.29 1.14 -3.48 0.972 3.71 -0.904 0.165
## 2255 1035 2659 1897 356 1238 2911 1557 2926 1382
## Predicted 62.55 81.12 70.66 49.46 74.311 69.0 61.44 67.46 56.128 72.32
## cvpred 62.62 80.69 70.76 48.96 74.072 69.1 61.56 67.35 56.098 72.17
## Life.expectancy 64.30 79.40 69.60 52.70 74.500 76.0 58.20 64.70 56.600 65.70
## CV residual 1.68 -1.29 -1.16 3.74 0.428 6.9 -3.36 -2.65 0.502 -6.47
## 515 1821 2439 199 1006 1214 571 689 1567 950
## Predicted 53.4 65.67 78.628 65.27 81.22 67.28 72.416 77.240 61.9 64.85
## cvpred 53.6 65.46 78.675 65.13 81.26 67.79 73.208 77.253 62.2 64.83
## Life.expectancy 49.9 67.00 79.500 69.50 79.10 65.30 73.900 78.100 59.9 63.50
## CV residual -3.7 1.54 0.825 4.37 -2.16 -2.49 0.692 0.847 -2.3 -1.33
##
## Sum of squares = 2875 Mean square = 12.4 n = 231
##
## fold 3
## Observations in test set: 231
## 1980 259 1078 2256 1528 397 491 1675 295 1623
## Predicted 64.17 73.40 59.90 62.2 75.60 73.77 60.52 72.185 60.91 58.86
## cvpred 64.32 73.14 59.95 62.3 75.41 73.74 60.13 72.046 60.86 58.83
## Life.expectancy 62.00 69.80 58.40 63.5 72.40 72.00 52.80 72.700 67.40 56.80
## CV residual -2.32 -3.34 -1.55 1.2 -3.01 -1.74 -7.33 0.654 6.54 -2.03
## 202 588 2507 2671 136 455 1492 1656 1112 2732
## Predicted 64.62 70.8 79.80 76.059 80.17 70.19 60.05 62.21 66.686 72.47
## cvpred 63.86 70.8 79.49 75.732 80.35 70.06 60.24 62.31 66.684 71.96
## Life.expectancy 68.20 72.8 82.30 74.800 84.00 72.40 58.10 62.20 65.900 78.00
## CV residual 4.34 2.0 2.81 -0.932 3.65 2.34 -2.14 -0.11 -0.784 6.04
## 1588 25 1079 2711 900 2137 952 407 42 942
## Predicted 72.95 73.33 63.54 62.11 76.40 73.686 63.68 56.968 72.805 78.86
## cvpred 72.91 73.11 63.27 62.26 76.12 73.835 63.78 57.111 72.901 78.99
## Life.expectancy 74.80 75.90 58.10 63.30 69.70 73.000 62.30 56.900 73.400 82.00
## CV residual 1.89 2.79 -5.17 1.04 -6.42 -0.835 -1.48 -0.211 0.499 3.01
## 143 500 1579 2672 111 1194 408 1205 1736 2139
## Predicted 77.44 81.902 49.71 76.35 71.32 59.85 56.350 70.97 76.628 72.44
## cvpred 77.44 82.061 49.91 76.05 71.32 58.14 56.417 70.86 76.298 72.58
## Life.expectancy 78.60 81.600 48.50 74.70 72.60 65.50 56.100 68.70 75.600 69.60
## CV residual 1.16 -0.461 -1.41 -1.35 1.28 7.36 -0.317 -2.16 -0.698 -2.98
## 459 240 1294 2436 1081 948 52 2583 426 1594
## Predicted 68.66 71.29 80.92 77.00 57.898 66.70 59.66 68.39 56.01 72.34
## cvpred 68.53 71.42 80.93 76.68 57.829 66.79 59.75 68.32 56.11 72.31
## Life.expectancy 71.80 68.00 89.00 81.00 57.300 65.50 56.00 71.40 54.10 73.80
## CV residual 3.27 -3.42 8.07 4.32 -0.529 -1.29 -3.75 3.08 -2.01 1.49
## 1606 1310 1676 934 1869 1607 1467 144 2209 1309
## Predicted 72.28 69.75 72.329 78.04 69.67 71.47 72.72 77.208 69.85 71.14
## cvpred 71.93 69.78 72.242 77.69 69.63 71.16 72.51 77.183 69.61 71.09
## Life.expectancy 77.60 73.30 72.900 81.50 72.50 77.30 74.40 78.100 72.20 73.50
## CV residual 5.67 3.52 0.658 3.81 2.87 6.14 1.89 0.917 2.59 2.41
## 2648 1822 1252 121 2661 2685 2377 1192 871 1069
## Predicted 73.91 65.47 81.08 82.471 73.2 74.800 64.17 63.86 78.19 69.996
## cvpred 73.89 65.36 80.79 82.126 72.9 74.718 64.38 62.53 78.12 69.798
## Life.expectancy 71.80 66.60 81.20 81.300 69.4 74.800 65.80 66.40 76.10 69.200
## CV residual -2.09 1.24 0.41 -0.826 -3.5 0.082 1.42 3.87 -2.02 -0.598
## 1362 406 1732 1036 2844 941 1601 2478 1988 2501
## Predicted 69.76 57.070 66.30 78.37 68.66 79.00 71.951 71.07 61.48 43.90
## cvpred 69.92 56.922 66.49 78.03 68.61 79.18 71.889 71.07 61.69 43.54
## Life.expectancy 63.90 57.500 62.80 79.70 71.70 81.00 72.700 76.00 59.60 45.60
## CV residual -6.02 0.578 -3.69 1.67 3.09 1.82 0.811 4.93 -2.09 2.06
## 131 2274 594 1065 270 233 1948 2011 1335 2400
## Predicted 78.06 72.849 68.69 68.33 70.56 71.97 66.054 73.03 74.067 56.516
## cvpred 77.74 72.845 68.37 68.35 70.59 71.75 65.838 72.95 73.906 56.624
## Life.expectancy 81.10 73.800 63.20 76.00 68.50 69.80 65.100 74.90 73.600 56.500
## CV residual 3.36 0.955 -5.17 7.65 -2.09 -1.95 -0.738 1.95 -0.306 -0.124
## 797 1755 552 1624 342 102 1787 1236 21 2643
## Predicted 72.29 70.15 76.40 58.14 64.53 71.85 61.27 67.795 73.68 73.008
## cvpred 72.19 70.13 76.17 58.08 64.66 71.81 61.08 67.799 73.54 72.779
## Life.expectancy 74.20 72.30 79.60 56.50 61.10 73.50 65.20 67.900 76.60 72.400
## CV residual 2.01 2.17 3.43 -1.58 -3.56 1.69 4.12 0.101 3.06 -0.379
## 566 2374 88 2219 585 1340 451 30 1625 269
## Predicted 73.85 63.79 77.43 67.011 71.68 75.21 73.222 72.934 57.92 72.92
## cvpred 73.56 63.83 77.33 66.843 71.65 75.03 72.922 72.747 57.87 72.72
## Life.expectancy 75.00 66.80 75.40 67.300 73.50 72.80 72.800 73.300 56.00 68.40
## CV residual 1.44 2.97 -1.93 0.457 1.85 -2.23 -0.122 0.553 -1.87 -4.32
## 676 2646 576 2728 2561 998 1144 1879 93 1874
## Predicted 76.43 72.49 70.49 52.67 68.48 77.40 69.97 56.55 77.1 68.87
## cvpred 76.28 72.39 70.15 52.79 68.44 77.15 69.87 56.54 76.9 68.86
## Life.expectancy 81.00 72.00 71.70 48.80 66.40 86.00 73.60 61.40 74.1 76.00
## CV residual 4.72 -0.39 1.55 -3.99 -2.04 8.85 3.73 4.86 -2.8 7.14
## 1899 2251 831 2068 1360 2261 2566 114 1789 858
## Predicted 48.52 63.98 73.46 79.83 70.44 60.42 67.87 88.71 62.88 58.06
## cvpred 47.99 63.95 73.21 79.55 70.57 60.53 67.91 88.52 62.97 58.36
## Life.expectancy 52.00 66.40 69.90 77.30 64.70 59.70 65.20 82.70 64.50 67.00
## CV residual 4.01 2.45 -3.31 -2.25 -5.87 -0.83 -2.71 -5.82 1.53 8.64
## 1240 386 603 452 628 148 1968 648 1447 86
## Predicted 69.2 74.944 63.87 71.12 74.57 72.020 72.7 76.230 75.76 76.97
## cvpred 69.2 74.878 63.93 70.94 74.32 72.019 72.5 75.897 75.69 76.75
## Life.expectancy 76.0 74.300 60.00 72.70 79.40 71.900 76.4 76.300 73.60 75.50
## CV residual 6.8 -0.578 -3.93 1.76 5.08 -0.119 3.9 0.403 -2.09 -1.25
## 107 1209 124 1380 1548 1945 775 2828 2030 98
## Predicted 68.91 69.69 82.60 72.10 83.4 65.12 73.781 70.61 68.670 73.78
## cvpred 68.85 69.65 82.07 72.03 83.7 64.42 73.635 70.57 68.904 73.58
## Life.expectancy 73.00 67.90 86.00 66.10 79.4 66.00 73.100 69.20 68.000 74.60
## CV residual 4.15 -1.75 3.93 -5.93 -4.3 1.58 -0.535 -1.37 -0.904 1.02
## 758 399 44 951 1024 100 2562 1562 2226 2301
## Predicted 59.9 75.96 73.459 64.2 63.36 72.33 68.55 63.41 66.079 60.7
## cvpred 60.0 75.77 73.276 64.2 63.06 72.28 68.52 63.44 66.045 60.8
## Life.expectancy 61.8 71.60 72.300 62.8 57.60 74.40 66.10 62.30 65.100 49.7
## CV residual 1.8 -4.17 -0.976 -1.4 -5.46 2.12 -2.42 -1.14 -0.945 -11.1
## 506 1792 1533 2564 418 2449 1660 1291 2292 1831
## Predicted 79.14 62.617 76.12 68.18 63.13 71.24 62.16 81.863 69.35 82.59
## cvpred 78.89 62.729 76.15 68.15 63.12 71.08 62.24 81.844 69.25 83.02
## Life.expectancy 85.00 63.500 78.00 65.50 59.10 72.30 61.20 81.300 72.20 81.70
## CV residual 6.11 0.771 1.85 -2.65 -4.02 1.22 -1.04 -0.544 2.95 -1.32
## 1604 2018 600 1725 1241 1867 756 402 2553 2121
## Predicted 73.65 71.963 64.29 73.83 69.36 68.71 60.59 59.908 69.5 76.00
## cvpred 73.16 71.824 64.28 73.59 69.45 68.55 60.68 59.969 69.5 75.95
## Life.expectancy 78.20 72.800 61.00 65.90 74.00 73.20 62.70 59.300 72.6 74.80
## CV residual 5.04 0.976 -3.28 -7.69 4.55 4.65 2.02 -0.669 3.1 -1.15
## 1529 2742 105 562 2500 1030 2448 2154 1791 1769
## Predicted 77.26 72.19 70.70 73.88 45.05 79.54 71.065 65.110 62.47 60.69
## cvpred 77.23 72.19 70.52 73.71 44.64 79.34 70.917 65.009 62.59 60.29
## Life.expectancy 72.20 67.40 73.50 75.80 46.00 84.00 71.800 65.200 63.90 54.30
## CV residual -5.03 -4.79 2.98 2.09 1.36 4.66 0.883 0.191 1.31 -5.99
## 503 798 326 1487 322 1589 1773 2305 339 1559
## Predicted 78.92 71.61 73.21 42.28 74.51 72.4 52.0174 56.4 67.79 64.233
## cvpred 78.62 71.33 72.79 42.53 74.23 72.3 52.1926 56.7 67.81 64.222
## Life.expectancy 81.00 74.40 76.40 45.50 77.20 74.6 52.1000 46.2 64.20 63.800
## CV residual 2.38 3.07 3.61 2.97 2.97 2.3 -0.0926 -10.5 -3.61 -0.422
## 1470 2609 1010 1825 1790 579 2690 875 1278 644
## Predicted 67.88 67.59 78.389 62.54 65.63 72.3 73.043 75.2 78.4 76.831
## cvpred 67.41 67.53 78.382 62.34 65.48 72.2 72.987 75.2 78.1 76.732
## Life.expectancy 73.70 66.20 78.000 64.70 64.20 74.4 73.200 73.0 81.0 77.700
## CV residual 6.29 -1.33 -0.382 2.36 -1.28 2.2 0.213 -2.2 2.9 0.968
## 1647 1540 785 1452 987 1483 32 1575 551 2576
## Predicted 78.11 82.37 69.56 76.47 74.036 45.985 73.033 56.87 76.41 73.301
## cvpred 78.04 82.83 69.48 76.51 73.724 46.393 72.835 56.91 76.17 73.088
## Life.expectancy 78.50 81.70 71.20 75.00 74.400 46.200 72.600 54.10 79.30 73.700
## CV residual 0.46 -1.13 1.72 -1.51 0.676 -0.193 -0.235 -2.81 3.13 0.612
## 2705 1303 331 467 1394 2134 2009 505 423 646
## Predicted 61.2 71.82 66.13 66.42 61.72 72.13 73.39 81.57 59.20 77.910
## cvpred 61.4 71.73 65.75 66.26 61.72 72.25 73.28 81.36 59.31 77.722
## Life.expectancy 64.5 75.20 75.00 67.80 64.10 78.00 75.30 85.00 56.20 77.000
## CV residual 3.1 3.47 9.25 1.54 2.38 5.75 2.02 3.64 -3.11 -0.722
## 2681
## Predicted 73.512
## cvpred 73.397
## Life.expectancy 72.900
## CV residual -0.497
##
## Sum of squares = 2623 Mean square = 11.4 n = 231
##
## fold 4
## Observations in test set: 231
## 55 24 2908 469 643 1474 238 1082 34 2837
## Predicted 56.40 73.79 64.15 68.91 76.915 68.44 71.21 61.63 76.26 70.14
## cvpred 56.52 73.86 64.04 69.39 77.275 68.59 71.08 62.03 76.57 69.94
## Life.expectancy 49.10 75.30 61.10 67.00 77.800 72.70 67.20 56.80 75.40 67.30
## CV residual -7.42 1.44 -2.94 -2.39 0.525 4.11 -3.88 -5.23 -1.17 -2.64
## 2141 2369 109 16 1681 1693 638 1817 1014 488
## Predicted 71.52 66.23 70.85 57.66 70.945 73.50 75.09 66.14 65.88 57.11
## cvpred 71.59 66.13 70.72 57.79 70.894 73.33 75.25 66.95 65.81 56.94
## Life.expectancy 68.40 68.00 72.70 54.80 71.500 75.80 78.00 68.90 61.60 54.20
## CV residual -3.19 1.87 1.98 -2.99 0.606 2.47 2.75 1.95 -4.21 -2.74
## 1448 2202 2582 914 687 2055 554 1384 1784 855 944
## Predicted 79.03 72.6 68.9 68.96 76.04 76.40 76.63 72.43 66.9 58.34 79.47
## cvpred 79.43 72.7 68.9 68.76 76.21 76.54 76.56 72.24 67.2 58.28 79.07
## Life.expectancy 72.80 73.8 71.7 67.70 78.40 73.70 78.90 65.30 65.9 62.90 79.20
## CV residual -6.63 1.1 2.8 -1.06 2.19 -2.84 2.34 -6.94 -1.3 4.62 0.13
## 2042 1536 327 2477 945 2 1355 1654 1678 800
## Predicted 76.215 78.53 71.92 71.062 80.49 63.00 71.92 63.80 71.740 71.95
## cvpred 76.634 78.89 72.42 71.091 80.59 63.62 71.55 64.31 71.689 71.72
## Life.expectancy 77.100 71.40 76.10 71.300 79.00 59.90 65.30 62.70 72.100 73.60
## CV residual 0.466 -7.49 3.68 0.209 -1.59 -3.72 -6.25 -1.61 0.411 1.88
## 2839 861 2835 2070 1881 2936 1991 1345 1882 956
## Predicted 69.99 58.620 70.12 78.89 56.53 48.42 60.106 74.57 55.61 61.5528
## cvpred 69.79 58.999 69.99 79.18 56.58 48.18 59.843 74.66 55.88 61.4307
## Life.expectancy 67.20 59.400 67.80 76.90 63.00 44.80 58.900 71.90 59.40 61.4000
## CV residual -2.59 0.401 -2.19 -2.28 6.42 -3.38 -0.943 -2.76 3.52 -0.0307
## 1595 152 773 1653 1950 122 627 2637 2260 590
## Predicted 72.14 71.43 71.46 65.28 64.599 86.15 74.58 74.037 60.45 71.00
## cvpred 72.12 71.28 71.35 65.52 65.248 86.29 74.76 73.888 60.63 70.92
## Life.expectancy 73.70 73.00 73.40 63.00 64.600 81.20 79.50 73.000 65.00 71.80
## CV residual 1.58 1.72 2.05 -2.52 -0.648 -5.09 4.74 -0.888 4.37 0.88
## 1611 1339 1349 1121 1671 1612 1143 2912 2216 2623 1076
## Predicted 70.9 76.65 75.72 66.50 73.569 71.28 70.02 60.0 74.6 62.09 60.07
## cvpred 71.3 76.85 75.75 66.67 73.522 71.73 70.13 60.1 74.5 62.05 60.28
## Life.expectancy 75.4 73.00 69.50 65.40 73.900 75.00 73.90 58.0 72.0 57.40 58.10
## CV residual 4.1 -3.85 -6.25 -1.27 0.378 3.27 3.77 -2.1 -2.5 -4.65 -2.18
## 106 2162 2035 517 1149 1068 1482 2847 1800 2375
## Predicted 70.80 62.28 68.84 52.80 69.02 69.875 47.765 68.6 66.73 67.218
## cvpred 70.65 62.62 68.96 52.72 69.01 70.282 47.349 68.5 66.92 67.378
## Life.expectancy 72.90 55.30 67.30 49.80 72.50 69.700 47.800 71.2 65.80 66.500
## CV residual 2.25 -7.32 -1.66 -2.92 3.49 -0.582 0.451 2.7 -1.12 -0.878
## 2019 2740 3 1578 1883 2409 1969 2838 2302 1955
## Predicted 72.031 71.84 63.05 50.507 54.33 56.154 73.38 70.18 59.7 62.453
## cvpred 71.883 71.89 63.69 49.866 54.39 56.431 73.34 69.99 60.0 62.646
## Life.expectancy 72.200 67.70 59.90 50.000 58.20 57.300 76.20 67.80 48.9 63.500
## CV residual 0.317 -4.19 -3.79 0.134 3.81 0.869 2.86 -2.19 -11.1 0.854
## 2647 251 1457 2704 2608 1376 1778 1949 2482 1655
## Predicted 73.94 79.246 74.57 61.4 68.12 52.168 50.1567 65.0208 72.69 63.4
## cvpred 73.71 79.408 74.62 61.4 68.17 51.785 49.8724 64.7901 72.82 63.9
## Life.expectancy 71.90 78.900 69.90 65.6 66.60 52.100 49.8000 64.8000 69.50 62.5
## CV residual -1.81 -0.508 -4.72 4.2 -1.57 0.315 -0.0724 0.0099 -3.32 -1.4
## 354 910 1680 1863 1466 1273 205 937 405 649
## Predicted 74.6335 72.21 71.32 70.38 74.103 78.99 64.1 80.8 57.450 76.675
## cvpred 74.7762 71.93 71.24 70.52 74.348 78.99 63.9 80.8 57.825 76.932
## Life.expectancy 74.8000 68.10 71.50 74.50 74.500 81.50 66.8 81.1 58.100 76.000
## CV residual 0.0238 -3.83 0.26 3.98 0.152 2.51 2.9 0.3 0.275 -0.932
## 2913 275 2041 1375 2215 936 1697 586 1391 1757
## Predicted 59.48 63.27 79.13 52.124 71.78 76.11 72.77 71.12 61.47 68.03
## cvpred 59.21 63.34 79.58 51.782 71.55 76.33 72.57 71.08 61.84 68.11
## Life.expectancy 57.40 59.50 77.30 52.400 75.00 81.30 75.00 73.10 64.70 71.40
## CV residual -1.81 -3.84 -2.28 0.618 3.45 4.97 2.43 2.02 2.86 3.29
## 1446 2049 630 2300 2551 574 2503 1206 1271 790
## Predicted 76.41 76.03 75.00 66.5 69.9 73.363 36.4 70.83 80.20 72.56
## cvpred 76.53 76.28 75.12 67.1 69.8 73.295 35.5 70.84 80.09 72.58
## Life.expectancy 73.80 75.20 79.00 54.0 72.8 72.700 46.4 68.50 81.80 75.50
## CV residual -2.73 -1.08 3.88 -13.1 3.0 -0.595 10.9 -2.34 1.71 2.92
## 2437 2745 2552 1983 2723 17 1776 149 254 997
## Predicted 80.122 71.78 69.8 67.0 61.0 74.64 50.11 71.68221 82.12 80.03
## cvpred 80.377 71.58 69.8 67.1 61.8 74.66 49.77 71.60361 82.31 80.55
## Life.expectancy 81.000 67.70 72.7 61.4 55.5 77.80 54.00 71.60000 78.00 86.00
## CV residual 0.623 -3.88 2.9 -5.7 -6.3 3.14 4.23 -0.00361 -4.31 5.45
## 1333 258 1944 828 2440 1751 1657 1007 2557
## Predicted 73.966 69.428 65.540 69.99 79.797 71.81 61.8170 80.26 69.137
## cvpred 74.036 69.396 65.957 69.83 79.928 71.99 61.9308 80.32 69.134
## Life.expectancy 73.900 70.000 66.200 75.00 79.400 73.90 62.0000 78.50 68.800
## CV residual -0.136 0.604 0.243 5.17 -0.528 1.91 0.0692 -1.82 -0.334
## 1218 2819 2493 2397 2674 1016 2567 11 575 2363
## Predicted 68.59 75.694 58.47 68.55 76.18 64.50 67.55 60.67 72.880 66.35
## cvpred 68.44 75.755 58.24 69.02 76.34 64.44 67.36 61.31 72.998 66.28
## Life.expectancy 66.30 75.400 56.50 59.20 74.60 69.00 64.30 57.30 72.200 68.80
## CV residual -2.14 -0.355 -1.74 -9.82 -1.74 4.56 -3.06 -4.01 -0.798 2.52
## 784 1687 1023 1672 2824 1300 404 2268 1282 1060
## Predicted 69.66 73.13 62.5 73.05 75.613 71.86 56.66 73.21 78.582 67.83
## cvpred 69.59 73.06 62.9 73.05 75.574 71.79 57.13 72.96 78.471 67.85
## Life.expectancy 71.40 76.30 57.9 73.60 75.400 75.80 58.60 75.30 78.900 71.70
## CV residual 1.81 3.24 -5.0 0.55 -0.174 4.01 1.47 2.34 0.429 3.85
## 2223 365 486 1386 2584 888 2161 639 343 2854
## Predicted 68.97 75.12 63.67 73.31 68.70 58.12 58.379 73.21 62.67 62.95
## cvpred 69.22 75.22 63.94 73.75 68.74 57.98 58.046 73.24 62.45 63.08
## Life.expectancy 66.20 71.80 55.30 65.10 71.20 61.80 57.600 78.30 59.20 69.60
## CV residual -3.02 -3.42 -8.64 -8.65 2.46 3.82 -0.446 5.06 -3.25 6.52
## 2290 1353 2048 2069 1381 1153 328 2016 2159 1196
## Predicted 71.429 72.85 75.935 80.16 72.28 67.99 73.39 71.35 62.10 65.38
## cvpred 71.289 72.56 76.155 80.52 72.11 67.89 73.56 71.18 62.19 67.17
## Life.expectancy 72.200 67.80 75.300 77.20 65.80 71.30 76.00 74.00 68.00 64.80
## CV residual 0.911 -4.76 -0.855 -3.32 -6.31 3.41 2.44 2.82 5.81 -2.37
## 1694 2142 1574 645 6 2818 1558 156 1198 2267
## Predicted 73.69 71.92 64.8 77.99 62.38 74.47 62.99 70.9 64.47 72.84
## cvpred 73.56 72.02 65.3 78.43 63.03 74.51 63.05 70.9 65.82 72.65
## Life.expectancy 75.30 68.20 55.3 77.10 58.80 76.40 64.30 68.4 64.00 75.40
## CV residual 1.74 -3.82 -10.0 -1.33 -4.23 1.89 1.25 -2.5 -1.82 2.75
## 1762 330 1346 1995 2938 685 2813 1779 2622 1152
## Predicted 70.178 74.819 74.30 70.22 38.11 76.98 76.12 55.8 67.44 67.2
## cvpred 70.385 75.002 74.38 69.99 37.44 77.19 76.24 55.9 67.75 67.1
## Life.expectancy 69.500 75.700 71.70 73.60 46.00 78.60 76.80 49.5 58.30 71.6
## CV residual -0.885 0.698 -2.68 3.61 8.56 1.41 0.56 -6.4 -9.45 4.5
## 2028 939 84 2032 2548 1987 580 1147 1699 1388
## Predicted 68.359 77.0 79.24 68.53 68.78 60.967 72.97 71.43 72.59 70.05
## cvpred 68.544 76.7 79.25 68.63 68.89 60.867 72.99 71.63 72.36 69.66
## Life.expectancy 68.000 89.0 75.90 67.50 73.50 59.900 74.30 73.00 74.80 65.00
## CV residual -0.544 12.3 -3.35 -1.13 4.61 -0.967 1.31 1.37 2.44 -4.66
## 2845 2724 2703 2816 1477 635 428 1734 2935 56
## Predicted 68.52 61.43 61.72 76.914 57.42 75.11 53.75 77.56 38.97 57.06
## cvpred 68.47 62.04 61.72 76.941 57.62 75.23 53.84 77.63 38.47 57.04
## Life.expectancy 71.60 54.90 65.80 76.300 52.10 78.00 52.60 75.90 44.50 48.70
## CV residual 3.13 -7.14 4.08 -0.641 -5.52 2.77 -1.24 -1.73 6.03 -8.34
##
## Sum of squares = 3313 Mean square = 14.3 n = 231
##
## fold 5
## Observations in test set: 231
## 1999 2286 569 647 1572 1034 1691 1077 2270 346
## Predicted 70.33 71.27 73.2 75.30 60.8 79.626 73.19 60.36 73.620 57.74
## cvpred 70.36 71.43 72.9 75.23 60.7 79.768 73.16 60.31 73.643 57.66
## Life.expectancy 72.70 72.60 74.4 76.60 57.6 79.900 75.60 58.80 74.600 54.80
## CV residual 2.34 1.17 1.5 1.37 -3.1 0.132 2.44 -1.51 0.957 -2.86
## 1598 400 41 905 2431 116 125 1494 90 591
## Predicted 72.560 73.83 71.48 75.80 79.44 88.18 84.04 60.53 76.92 69.69
## cvpred 72.478 73.71 71.44 75.97 79.22 88.52 84.17 60.43 77.08 69.42
## Life.expectancy 73.200 71.10 73.80 68.90 81.90 82.30 83.00 67.00 75.20 71.50
## CV residual 0.722 -2.61 2.36 -7.07 2.68 -6.22 -1.17 6.57 -1.88 2.08
## 1994 827 1343 1253 2153 2833 1621 2604 1341 2444
## Predicted 69.55 72.65 74.83 81.150 68.29 69.21 58.92 68.581 75.09 71.79
## cvpred 69.73 72.84 74.72 81.033 68.48 69.23 58.89 68.624 74.97 71.73
## Life.expectancy 73.80 71.20 72.30 81.000 65.70 68.00 57.30 67.700 72.40 74.60
## CV residual 4.07 -1.64 -2.42 -0.033 -2.78 -1.23 -1.59 -0.924 -2.57 2.87
## 1387 2126 1040 1368 2547 1758 255 1256 1990 2683
## Predicted 71.25 75.51 76.84 60.53 69.08 69.48 84.46 83.28 60.61 76.444
## cvpred 71.09 75.38 76.86 60.35 68.82 69.52 84.48 83.21 60.42 76.438
## Life.expectancy 65.00 73.10 79.00 63.00 73.70 71.00 78.00 86.00 59.10 75.500
## CV residual -6.09 -2.28 2.14 2.65 4.88 1.48 -6.48 2.79 -1.32 -0.938
## 2502 2605 2071 1304 2693 1334 799 1038 246 249
## Predicted 44.807 68.70 77.9 70.8 72.387 73.722 72.22 77.56 77.90 77.33
## cvpred 45.103 68.75 77.9 70.8 72.308 73.565 72.23 77.56 77.89 77.15
## Life.expectancy 45.900 67.40 76.6 75.0 72.000 73.700 74.40 79.20 80.00 79.50
## CV residual 0.797 -1.35 -1.3 4.2 -0.308 0.135 2.17 1.64 2.11 2.35
## 420 284 1039 1119 1580 2125 2505 2653 1971 38
## Predicted 62.56 60.18 78.120 65.701 48.58 76.55 39.10 71.69 73.63 73.970
## cvpred 62.64 60.23 78.255 65.448 48.55 76.43 39.08 71.62 73.62 73.935
## Life.expectancy 58.00 56.10 79.100 65.300 47.10 73.40 48.40 78.00 75.80 74.700
## CV residual -4.64 -4.13 0.845 -0.148 -1.45 -3.03 9.32 6.38 2.18 0.765
## 1458 1276 2138 304 532 2003 1824 1764 2744 419
## Predicted 74.2 78.7 73.48 57.72 54.16 70.844 67.38 69.517 72.21 67.06
## cvpred 74.0 78.6 73.47 58.23 53.92 70.903 67.43 69.586 72.18 67.35
## Life.expectancy 71.0 84.0 70.00 62.00 51.80 71.900 65.40 68.600 67.60 58.60
## CV residual -3.0 5.4 -3.47 3.77 -2.12 0.997 -2.03 -0.986 -4.58 -8.75
## 274 1636 2924 2046 2054 1767 1111 2925 348 2722
## Predicted 63.66 77.73 59.432 76.734 76.73 62.97 66.79 58.255 49.196 61.92
## cvpred 63.72 77.36 59.489 76.606 76.58 63.25 66.81 58.339 49.091 62.32
## Life.expectancy 59.70 81.40 59.200 75.700 74.20 55.30 65.60 58.000 48.100 56.30
## CV residual -4.02 4.04 -0.289 -0.906 -2.38 -7.95 -1.21 -0.339 -0.991 -6.02
## 1537 1269 338 519 1600 2696 2130 1306 2814 982
## Predicted 77.84 80.45 68.54 52.12 73.93 73.54 74.29 71.94 75.914 74.7
## cvpred 77.85 80.44 68.37 51.97 73.94 73.41 74.09 71.92 75.908 74.7
## Life.expectancy 71.20 82.10 65.10 48.60 72.90 78.00 71.90 74.50 76.500 74.2
## CV residual -6.65 1.66 -3.27 -3.37 -1.04 4.59 -2.19 2.58 0.592 -0.5
## 1211 1771 2651 198 358 2738 1730 410 2157 1880
## Predicted 71.22 60.11 71.764 65.77 74.123 70.39 67.79 59.48 66.2 56.8
## cvpred 71.11 60.52 71.688 65.85 74.081 70.18 67.76 59.72 66.6 56.8
## Life.expectancy 67.50 53.80 71.100 69.90 73.800 67.70 63.80 54.30 62.8 69.0
## CV residual -3.61 -6.72 -0.588 4.05 -0.281 -2.48 -3.96 -5.42 -3.8 12.2
## 141 1268 403 1964 1019 1301 679 2140 1722 2848
## Predicted 76.39 81.295 62.8 72.67 66.50 71.68 77.21 72.02 74.50 68.72
## cvpred 76.38 81.318 63.1 72.61 66.71 71.64 77.04 71.98 74.75 68.68
## Life.expectancy 78.80 82.200 59.0 77.30 59.90 75.60 79.50 69.40 66.30 71.00
## CV residual 2.42 0.882 -4.1 4.69 -6.81 3.96 2.46 -2.58 -8.45 2.32
## 363 1197 2496 357 1641 2508 2020 1989 1453 1984
## Predicted 74.08 62.46 53.42 74.372 76.9 79.90 72.820 61.25 76.043 62.8
## cvpred 74.07 62.55 53.67 74.298 76.6 79.51 72.913 60.93 75.878 62.8
## Life.expectancy 72.70 64.40 52.60 74.100 82.0 81.90 72.100 59.30 76.000 61.1
## CV residual -1.37 1.85 -1.07 -0.198 5.4 2.39 -0.813 -1.63 0.122 -1.7
## 2574 1583 778 325 1550 1739 1461 2669 2735 104
## Predicted 71.5 46.75 70.51 73.47 82.12 75.182 73.72 76.36 73.99 72.204
## cvpred 71.6 46.78 70.57 73.42 82.43 75.194 73.53 76.43 73.86 72.323
## Life.expectancy 74.1 44.60 73.30 76.90 78.70 75.000 74.90 74.90 75.00 73.200
## CV residual 2.5 -2.18 2.73 3.48 -3.73 -0.194 1.37 -1.53 1.14 0.877
## 10 1374 2452 2581 2285 1450 2721 1293 859 794
## Predicted 60.68 53.42 71.71 69.56 72.490 76.44 57.450 81.29 57.85 72.59
## cvpred 60.56 53.42 71.69 69.66 72.318 76.25 57.622 81.21 57.83 72.63
## Life.expectancy 57.30 53.00 74.20 71.60 72.700 71.90 57.500 88.00 62.00 74.60
## CV residual -3.26 -0.42 2.51 1.94 0.382 -4.35 -0.122 6.79 4.17 1.97
## 142 227 890 2062 1008 1688 2368 1332 473 2026
## Predicted 80.58 76.51 55.98 78.06 78.564 71.97 66.66 73.660 67.9 68.335
## cvpred 80.84 76.85 56.19 78.23 78.528 72.03 66.68 73.521 68.1 68.222
## Life.expectancy 78.70 71.70 59.80 79.30 78.400 76.10 68.10 74.000 65.0 68.100
## CV residual -2.14 -5.15 3.61 1.07 -0.128 4.07 1.42 0.479 -3.1 -0.122
## 1003 135 91 103 514 2211 2454 874 1617 1444
## Predicted 82.13 81.282 77.01 70.2 54.09 73.68 71.80 74.933 70.2 76.23
## cvpred 82.42 81.295 77.13 70.2 53.93 73.71 71.75 75.156 70.3 75.89
## Life.expectancy 79.80 82.000 74.90 73.3 58.00 71.60 73.90 74.200 78.0 74.40
## CV residual -2.62 0.705 -2.23 3.1 4.07 -2.11 2.15 -0.956 7.7 -1.49
## 456 1637 1020 368 323 1871 1547 2135 1061 2483
## Predicted 70.08 77.20 61.7 74.795 75.51 71.46 76.41 72.02 68.32 69.745
## cvpred 70.28 76.92 61.7 74.884 75.51 71.63 76.18 71.91 68.26 69.672
## Life.expectancy 72.40 81.10 59.4 75.000 77.00 73.00 79.70 77.00 71.40 69.300
## CV residual 2.12 4.18 -2.3 0.116 1.49 1.37 3.52 5.09 3.14 -0.372
## 2559 1834 873 261 2673 157 2277 760 2229 291
## Predicted 69.08 80.249 76.00 70.37 76.01 70.58 73.405 59.1 65.86 67.78
## cvpred 69.04 80.155 76.22 70.41 76.14 70.39 73.431 58.9 65.84 67.78
## Life.expectancy 67.30 81.100 74.90 69.40 74.70 67.80 73.000 69.0 63.80 69.10
## CV residual -1.74 0.945 -1.32 -1.01 -1.44 -2.59 -0.431 10.1 -2.04 1.32
## 2398 2642 1685 993 876 2680 1613 2826 1729 1371
## Predicted 62.12 72.856 73.0 72.424 74.80 75.29 71.66 73.56 67.10 57.99
## cvpred 61.91 72.938 73.0 72.355 75.02 75.47 71.64 73.35 67.05 58.05
## Life.expectancy 58.90 72.500 76.6 73.000 73.00 73.20 74.30 75.10 64.00 56.80
## CV residual -3.01 -0.438 3.6 0.645 -2.02 -2.27 2.66 1.75 -3.05 -1.25
## 1866 2858 2057 2404 2701 280 1190 1359 2306 2815
## Predicted 68.84 64.71 77.0 50.8 71.32 61.63 72.34 70.70 61.8 76.221
## cvpred 68.93 65.61 76.8 50.8 71.46 61.68 73.17 70.76 62.2 76.197
## Life.expectancy 74.50 69.00 89.0 53.8 65.60 57.60 67.30 64.40 45.3 77.000
## CV residual 5.57 3.39 12.2 3.0 -5.86 -4.08 -5.87 -6.36 -16.9 0.803
## 2655 57 393 1451 26 530 2146 2914 1116 1801
## Predicted 70.24 56.7 72.605 75.84 70.42 55.09 70.84 62.59 71.13 64.4394
## cvpred 69.83 56.8 72.493 75.68 70.49 54.93 70.81 62.96 71.41 64.3662
## Life.expectancy 74.00 48.2 72.600 78.00 74.20 52.60 65.00 55.70 65.20 64.3000
## CV residual 4.17 -8.6 0.107 2.32 3.71 -2.33 -5.81 -7.26 -6.21 -0.0662
## 1460 290 1986 1296 1037 82 1875 629 2649 1596
## Predicted 73.69 67.87 66.16 79.838 77.14 77.39 68.58 74.71 74.29 72.47
## cvpred 73.48 67.87 66.28 79.709 77.31 77.51 68.64 74.75 74.37 72.39
## Life.expectancy 74.80 69.40 64.00 80.000 79.30 76.20 75.00 79.20 71.60 73.60
## CV residual 1.32 1.53 -2.28 0.291 1.99 -1.31 6.36 4.45 -2.77 1.21
## 1365 1383 19 1498 1661 1750 1645 1568 2376 2667
## Predicted 63.45 72.47 74.59 62.48 61.79 71.8 79.2409 61.94 63.8 74.650
## cvpred 63.48 72.75 74.66 62.47 61.74 71.8 79.0703 61.82 63.8 74.741
## Life.expectancy 62.60 65.50 77.20 58.60 69.00 74.1 79.0000 59.30 66.2 75.100
## CV residual -0.88 -7.25 2.54 -3.87 7.26 2.3 -0.0703 -2.52 2.4 0.359
## 2129
## Predicted 74.56
## cvpred 74.41
## Life.expectancy 72.50
## CV residual -1.91
##
## Sum of squares = 3243 Mean square = 14 n = 231
##
## Overall (Sum over all 231 folds)
## ms
## 12.6mean((data.test$Life.expectancy - predict(model.additive, data.test)) ^ 2)## [1] 13.5model.selected = step(lm(Life.expectancy ~ ., data.train), trace = FALSE)
cv.lm(data.train, model.selected, m = 5, plotit = FALSE)## Analysis of Variance Table
##
## Response: Life.expectancy
## Df Sum Sq Mean Sq F value Pr(>F)
## Year 1 417 417 33.72 8.2e-09 ***
## Status 1 17517 17517 1415.45 < 2e-16 ***
## Adult.Mortality 1 28083 28083 2269.20 < 2e-16 ***
## infant.deaths 1 1105 1105 89.29 < 2e-16 ***
## Alcohol 1 2219 2219 179.28 < 2e-16 ***
## percentage.expenditure 1 1108 1108 89.55 < 2e-16 ***
## BMI 1 3790 3790 306.21 < 2e-16 ***
## under.five.deaths 1 2965 2965 239.62 < 2e-16 ***
## Total.expenditure 1 32 32 2.55 0.11
## Diphtheria 1 1215 1215 98.16 < 2e-16 ***
## HIV.AIDS 1 6689 6689 540.49 < 2e-16 ***
## Income.composition.of.resources 1 4907 4907 396.52 < 2e-16 ***
## Schooling 1 2122 2122 171.49 < 2e-16 ***
## Residuals 1140 14108 12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## fold 1
## Observations in test set: 230
## 2275 2699 2124 834 2276 2697 884 1289 2160 1354
## Predicted 73.716 68.36 76.0 70.22 73.499 71.3 60.54 80.33 61.1 72.42
## cvpred 73.905 68.36 75.9 70.31 73.666 71.4 60.46 80.21 61.0 72.45
## Life.expectancy 73.600 66.00 74.3 69.00 73.000 74.0 64.20 81.60 59.6 66.60
## CV residual -0.305 -2.36 -1.6 -1.31 -0.666 2.6 3.74 1.39 -1.4 -5.85
## 1727 1140 1295 1590 508 1629 1366 2043 2258 688
## Predicted 69.11 68.22 80.310 72.56 79.375 60.52 63.39 76.428 63.79 75.49
## cvpred 69.14 68.25 80.257 72.64 79.538 60.48 63.31 76.335 63.68 75.38
## Life.expectancy 64.50 74.50 79.900 74.50 80.000 53.60 62.10 76.800 62.10 78.20
## CV residual -4.64 6.25 -0.357 1.86 0.462 -6.88 -1.21 0.465 -1.58 2.82
## 2709 2694 2855 1337 1348 824 283 392 1110 1721
## Predicted 60.43 72.094 62.42 73.442 75.82 71.281 59.06 74.30 70.30 72.37
## cvpred 59.95 72.215 62.07 73.563 75.94 71.386 58.99 74.18 70.39 72.41
## Life.expectancy 63.50 71.600 69.40 73.300 69.90 72.000 56.50 72.90 65.80 67.30
## CV residual 3.55 -0.615 7.33 -0.263 -6.04 0.614 -2.49 -1.28 -4.59 -5.11
## 277 1979 299 92 1826 1002 1193 779 2206 2064
## Predicted 62.77 64.10 59.69 79.12 67.8 83.54 69.18 68.98 72.137 77.29
## cvpred 62.69 64.08 59.28 79.27 67.7 83.34 69.31 68.95 72.304 77.23
## Life.expectancy 59.10 62.20 65.00 74.70 64.3 79.90 66.00 72.90 72.600 78.70
## CV residual -3.59 -1.88 5.72 -4.57 -3.4 -3.44 -3.31 3.95 0.296 1.47
## 1493 2257 118 265 361 1963 1772 388 2852 634
## Predicted 63.36 61.05 86.66 70.88 73.740 74.14 58.8 75.08 68.27 73.71
## cvpred 63.35 60.92 86.64 70.93 73.867 74.35 58.8 74.98 68.29 73.91
## Life.expectancy 61.10 62.80 81.90 69.60 73.300 77.20 53.2 73.90 71.00 78.90
## CV residual -2.25 1.88 -4.74 -1.33 -0.567 2.85 -5.6 -1.08 2.71 4.99
## 1674 2928 2572 602 1682 300 203 474 826
## Predicted 71.820 52.009 71.84 64.26 70.73 58.99 64.80 63.280 71.7159
## cvpred 71.803 51.975 71.85 64.14 70.71 58.57 64.69 63.242 71.7874
## Life.expectancy 72.800 52.400 74.50 63.00 71.50 64.20 67.80 64.100 71.7000
## CV residual 0.997 0.425 2.65 -1.14 0.79 5.63 3.11 0.858 -0.0874
## 2144 1966 1288 1723 2817 796 204 83 230 2931
## Predicted 71.03 73.0 82.91 71.12 75.0 72.39 64.70 77.41 72.9935 54.58
## cvpred 71.11 73.2 82.92 71.16 75.1 72.48 64.58 77.54 73.0819 54.67
## Life.expectancy 67.30 76.8 81.80 66.90 76.6 74.40 67.30 76.00 73.0000 46.60
## CV residual -3.81 3.6 -1.12 -4.26 1.5 1.92 2.72 -1.54 -0.0819 -8.07
## 2029 147 1022 1768 2725 427 2829 2002 293 547
## Predicted 67.796 70.30 62.80 62.00 55.42 54.92 70.52 70.8 67.603 77.53
## cvpred 67.793 70.34 62.85 61.98 55.43 54.84 70.61 70.9 67.539 77.75
## Life.expectancy 67.900 72.20 58.30 54.80 53.20 53.40 69.10 72.1 68.300 81.00
## CV residual 0.107 1.86 -4.55 -7.18 -2.23 -1.44 -1.51 1.2 0.761 3.25
## 2228 1618 134 1967 1615 1997 2737 1970 1216 8
## Predicted 64.763 70.312 81.15 72.98 70.90 71.17 72.42 72.1 67.115 62.08
## cvpred 64.597 70.325 81.16 73.13 70.88 71.31 72.58 72.2 67.123 62.06
## Life.expectancy 64.300 69.600 84.00 76.50 72.70 73.20 69.20 75.8 66.700 58.10
## CV residual -0.297 -0.725 2.84 3.37 1.82 1.89 -3.38 3.6 -0.423 -3.96
## 1532 1336 421 1777 862 235 2033 394 1465 1150
## Predicted 75.91 74.60 61.43 50.119 53.56 72.16 67.729 72.581 74.172 68.49
## cvpred 75.76 74.81 61.33 50.081 53.13 72.25 67.658 72.338 74.388 68.57
## Life.expectancy 76.00 73.40 57.40 51.000 59.10 68.10 67.300 72.200 74.700 72.20
## CV residual 0.24 -1.41 -3.93 0.919 5.97 -4.15 -0.358 -0.138 0.312 3.63
## 2692 2733 908 1191 133 279 592 18 272 2679
## Predicted 71.0 71.083 72.72 62.07 80.81 62.28 70.930 75.63 69.312 75.38
## cvpred 71.2 71.133 72.76 62.19 80.61 62.18 71.012 75.78 69.252 75.47
## Life.expectancy 72.4 71.000 68.50 66.80 88.00 58.40 71.400 77.50 68.300 73.50
## CV residual 1.2 -0.133 -4.26 4.61 7.39 -3.78 0.388 1.72 -0.952 -1.97
## 886 462 909 864 1534 2291 681 1242 87 2585
## Predicted 59.55 68.9 72.68 51.33 79.04 70.28 76.32 69.056 77.37 68.57
## cvpred 59.49 68.9 72.72 51.02 78.91 70.22 76.25 69.132 77.54 68.51
## Life.expectancy 63.30 77.0 68.30 58.50 71.60 72.20 79.10 69.300 75.60 71.10
## CV residual 3.81 8.1 -4.42 7.48 -7.31 1.98 2.85 0.168 -1.94 2.59
## 1952 833 567 1531 1541 2133 1125 126 872
## Predicted 64.432 70.35 74.014 79.57 81.763 72.35 63.345 83.66 76.237
## cvpred 64.386 70.44 74.058 79.45 81.566 72.14 63.391 83.64 76.375
## Life.expectancy 64.200 68.90 74.900 72.00 81.400 77.00 62.700 79.90 75.600
## CV residual -0.186 -1.54 0.842 -7.45 -0.166 4.86 -0.691 -3.74 -0.775
## 1544 2059 795 2658 359 1 2149 36 2910
## Predicted 77.50 78.10 74.320 70.77 73.952 63.58 70.30 74.95774 62.39
## cvpred 77.47 78.07 74.435 70.86 74.098 63.58 70.37 75.09319 62.35
## Life.expectancy 86.00 83.00 74.700 69.70 73.600 65.00 64.80 75.10000 59.20
## CV residual 8.53 4.93 0.265 -1.16 -0.498 1.42 -5.57 0.00681 -3.15
## 1642 2850 2812 1832 2155 2577 1626 237 1627 1237
## Predicted 78.36 68.42 75.808 82.88 65.140 71.11 57.04 69.61 57.60 71.22
## cvpred 78.35 68.44 76.027 82.96 65.092 71.09 56.98 69.77 57.54 71.39
## Life.expectancy 80.00 75.00 76.800 81.40 64.600 73.50 55.50 67.70 55.00 69.50
## CV residual 1.65 6.56 0.773 -1.56 -0.492 2.41 -1.48 -2.07 -2.54 -1.89
## 458 1393 1497 470 1189 2025 507 1207 14 1551
## Predicted 69.65 63.82 63.0 66.288 67.85 67.565 81.468 70.25 63.15 81.24
## cvpred 69.62 63.61 63.1 66.225 67.92 67.593 81.745 70.22 63.16 81.16
## Life.expectancy 72.10 64.30 59.2 66.600 67.60 68.400 81.000 68.30 56.20 78.60
## CV residual 2.48 0.69 -3.9 0.375 -0.32 0.807 -0.745 -1.92 -6.96 -2.56
## 1895 536 266 2395 364 2638 2475 22 2619 350
## Predicted 51.66 52.15 70.66 65.01 76.60 75.9 71.026 72.71 64.84 45.121
## cvpred 51.76 52.04 70.69 65.06 76.72 76.1 71.144 72.83 64.74 45.281
## Life.expectancy 53.60 49.60 69.40 62.00 72.00 72.9 71.400 76.20 59.70 46.000
## CV residual 1.84 -2.44 -1.29 -3.06 -4.72 -3.2 0.256 3.37 -5.04 0.719
## 367 2702 2856 1819 1616 550 301 244 2558 352 110
## Predicted 74.80 68.17 60.9 67.03 70.7 74.38 58.89 78.2 69.012 44.03 70.81
## cvpred 74.87 68.15 60.6 66.99 70.7 74.46 58.48 78.0 69.049 44.19 70.88
## Life.expectancy 71.00 65.60 69.3 68.00 71.8 79.10 63.30 83.0 68.100 47.80 72.60
## CV residual -3.87 -2.55 8.7 1.01 1.1 4.64 4.82 5.0 -0.949 3.61 1.72
## 138 2128 1565 2494 1631 1000 2640 2031 39 1287
## Predicted 76.41 74.89 63.08 55.530 55.25 83.18 74.21 68.318 73.482 82.900
## cvpred 76.21 74.72 62.99 55.567 55.17 83.21 74.33 68.302 73.586 82.903
## Life.expectancy 79.80 72.90 69.00 55.000 52.00 81.00 72.50 67.500 74.400 82.000
## CV residual 3.59 -1.82 6.01 -0.567 -3.17 -2.21 -1.83 -0.802 0.814 -0.903
## 1833 597 137 1582 2652 2606 2832 1141 2165
## Predicted 80.174 65.32 81.069 46.99 71.119 68.303 68.964 72.02 53.76
## cvpred 80.121 65.25 80.857 47.01 71.245 68.185 68.927 72.17 53.59
## Life.expectancy 81.100 62.20 81.000 45.10 71.000 67.200 68.300 74.30 57.00
## CV residual 0.979 -3.05 0.143 -1.91 -0.245 -0.985 -0.627 2.13 3.41
## 387 2401 2555 911 13 1274 37 472 2145 786
## Predicted 76.63 54.215 69.267 75.23 59.31 78.8 74.467 66.20 75.40 69.75
## cvpred 76.57 54.436 69.337 75.29 59.31 79.1 74.578 66.12 75.52 69.83
## Life.expectancy 74.10 55.300 69.600 68.00 56.70 81.0 74.900 65.60 66.40 72.00
## CV residual -2.47 0.864 0.263 -7.29 -2.61 1.9 0.322 -0.52 -9.12 2.17
## 2001 2657 2603 632 901 2402 1290 2367 1646 489
## Predicted 70.70 68.78 68.506 73.89 73.84 52.55 79.66 64.38 77.6 55.89
## cvpred 70.76 68.85 68.402 74.13 73.91 52.78 79.66 64.49 77.6 55.83
## Life.expectancy 72.30 69.90 68.000 79.20 69.60 54.50 81.50 68.30 78.7 53.60
## CV residual 1.54 1.05 -0.402 5.07 -4.31 1.72 1.84 3.81 1.1 -2.23
## 2834 2289 2840 197 2013 1015 1018 1689 243 531
## Predicted 70.3 71.484 69.8 68.46 74.321 65.10 63.496 71.65 78.00 55.0
## cvpred 70.3 71.466 69.8 68.39 74.431 65.06 63.445 71.69 77.83 54.9
## Life.expectancy 67.9 72.200 67.1 73.00 73.700 61.20 63.000 75.60 87.00 52.2
## CV residual -2.4 0.734 -2.7 4.61 -0.731 -3.86 -0.445 3.91 9.17 -2.7
## 12 1614 2204
## Predicted 58.91 72.796 72.448
## cvpred 58.94 72.802 72.619
## Life.expectancy 57.00 73.400 73.200
## CV residual -1.94 0.598 0.581
##
## Sum of squares = 2527 Mean square = 11 n = 230
##
## fold 2
## Observations in test set: 231
## 1108 2718 1609 2297 2933 2015 2405 2429 1677 605
## Predicted 66.535 59.935 71.49 63.96 41.67 70.86 51.22 81.864 72.232 57.77
## cvpred 66.467 59.878 71.45 62.72 41.89 70.98 51.32 81.689 72.328 57.13
## Life.expectancy 66.000 60.000 76.30 71.80 44.60 73.90 53.70 82.000 71.800 59.60
## CV residual -0.467 0.122 4.85 9.08 2.71 2.92 2.38 0.311 -0.528 2.47
## 2447 1740 1243 139 146 1696 1673 2736 2163 1718
## Predicted 72.10 74.880 67.74 79.130 72.3942 73.28 71.67 72.21 55.62 72.80
## cvpred 72.29 74.828 67.98 79.147 72.5289 73.28 71.87 72.11 55.43 72.88
## Life.expectancy 74.50 74.600 65.90 79.400 72.5000 75.00 73.30 69.80 53.40 68.40
## CV residual 2.21 -0.228 -2.08 0.253 -0.0289 1.72 1.43 -2.31 -2.03 -4.48
## 2365 2434 466 242 1690 468 1281 777 1962 2707
## Predicted 66.45 79.03 66.95 80.77 75.138 66.686 78.445 70.98 71.75 61.15
## cvpred 66.31 79.02 66.96 80.66 75.037 66.694 78.572 70.94 71.79 60.13
## Life.expectancy 68.70 89.00 68.30 89.00 75.700 67.400 79.300 73.60 77.50 63.70
## CV residual 2.39 9.98 1.34 8.34 0.663 0.706 0.728 2.66 5.71 3.57
## 43 583 1530 1358 461 1114 1462 1154 1904
## Predicted 71.890 74.242 76.78 70.61 68.85 66.487 74.114 67.69 50.934
## cvpred 72.044 74.077 76.74 70.76 68.79 66.496 74.155 67.64 49.717
## Life.expectancy 72.900 73.600 71.10 64.70 71.10 66.300 75.000 71.00 49.200
## CV residual 0.856 -0.477 -5.64 -6.06 2.31 -0.196 0.845 3.36 -0.517
## 1094 1357 1903 1686 534 2222 1974 989 1756 1255
## Predicted 60.12 71.41 44.61 74.54 53.93 66.20 73.38 72.2 69.89 84.800
## cvpred 60.03 71.49 43.76 74.48 53.95 66.06 73.37 72.2 69.85 84.531
## Life.expectancy 57.60 64.60 49.80 76.60 51.20 66.60 75.50 73.9 71.80 84.000
## CV residual -2.43 -6.89 6.04 2.12 -2.75 0.54 2.13 1.7 1.95 -0.531
## 2061 1754 276 2296 345 1947 1239 1643 264 1280
## Predicted 78.13 71.91 61.48 71.200 59.53 65.542 69.4 78.24 71.06 77.46
## cvpred 78.08 71.78 61.52 71.314 59.69 65.826 69.5 78.25 71.02 77.69
## Life.expectancy 79.60 72.80 59.30 72.000 56.90 65.500 77.0 79.60 69.60 79.30
## CV residual 1.52 1.02 -2.22 0.686 -2.79 -0.326 7.5 1.35 -1.42 1.61
## 263 793 2445 2663 1244 1593 2065 1456 256 1527
## Predicted 71.05 71.12 71.94 70.04 67.42 72.52 78.447 75.27 82.66 77.98
## cvpred 70.99 71.25 72.14 70.21 67.69 72.76 78.245 75.39 82.62 77.99
## Life.expectancy 69.50 75.10 74.50 69.20 64.70 74.00 78.500 73.00 77.60 72.80
## CV residual -1.49 3.85 2.36 -1.01 -2.99 1.24 0.255 -2.39 -5.02 -5.19
## 2509 2284 1212 252 1605 902 1083 1793 1210 2123
## Predicted 84.41 72.779 68.99 84.05 73.22 71.99 62.65 62.377 69.63 76.03
## cvpred 84.14 72.976 69.33 83.81 73.11 72.18 62.42 62.473 69.93 76.08
## Life.expectancy 81.70 72.900 67.30 78.80 77.90 69.40 56.40 63.200 67.70 74.40
## CV residual -2.44 -0.076 -2.03 -5.01 4.79 -2.78 -6.02 0.727 -2.23 -1.68
## 130 1610 1338 282 1476 2443 1351 27 932 1538
## Predicted 82.107 71.27 73.340 61.32 56.57 72.26 72.51 72.56 80.71 77.82
## cvpred 81.802 71.24 73.496 61.29 56.76 72.45 72.56 72.49 80.28 77.77
## Life.expectancy 81.400 75.90 73.100 56.80 52.10 74.70 68.50 73.50 82.20 71.60
## CV residual -0.402 4.66 -0.396 -4.49 -4.66 2.25 -4.06 1.01 1.92 -6.17
## 1973 868 933 589 1120 1464 686 390 119 2406
## Predicted 73.42 78.6 80.81 73.52 66.96 74.559 76.09 74.73 85.61 51.88
## cvpred 73.38 78.7 80.39 73.42 66.92 74.563 76.23 74.72 85.36 51.99
## Life.expectancy 75.70 77.3 82.00 72.40 65.30 74.900 78.50 73.40 81.70 54.00
## CV residual 2.32 -1.4 1.61 -1.02 -1.62 0.337 2.27 -1.32 -3.66 2.01
## 2831 953 878 1064 518 863 568 1213 2225 935
## Predicted 70.23 67.35 74.47 68.36 52.28 53.30 73.840 71.71 66.036 76.29
## cvpred 70.26 67.26 74.33 68.32 52.45 52.74 74.083 71.92 65.932 76.26
## Life.expectancy 68.50 61.70 72.30 77.00 49.20 58.80 74.500 67.20 65.400 81.70
## CV residual -1.76 -5.56 -2.03 8.68 -3.25 6.06 0.417 -4.72 -0.532 5.44
## 949 994 2624 857 1217 1284 2269 40 302 2689 501
## Predicted 65.98 63.27 60.73 57.92 68.70 81.34 74.01 72.7 58.77 71.56 77.6
## cvpred 66.01 62.23 60.69 58.03 69.01 81.24 73.79 72.8 57.96 71.76 77.7
## Life.expectancy 64.60 71.80 56.70 61.40 66.50 82.50 74.90 74.1 62.50 73.50 81.5
## CV residual -1.41 9.57 -3.99 3.37 -2.51 1.26 1.11 1.3 4.54 1.74 3.8
## 2294 1573 1469 891 2499 2366 2207 1286 1872 1471
## Predicted 70.98 58.9 67.29 57.922 40.05 66.36 71.36 82.678 68.82 70.18
## cvpred 71.05 59.0 66.02 57.588 40.33 66.19 71.39 82.542 68.75 68.69
## Life.expectancy 72.10 56.7 73.90 58.500 47.80 68.50 76.00 82.000 71.20 73.50
## CV residual 1.05 -2.3 7.88 0.912 7.47 2.31 4.61 -0.542 2.45 4.81
## 2695 2909 2580 2563 2230 2550 1662 2607 1524 260
## Predicted 71.792 63.307 69.92 68.30 65.52 69.64 62.09 68.42 76.9 70.57
## cvpred 71.877 63.338 70.03 68.35 65.28 69.67 62.18 68.59 76.8 70.52
## Life.expectancy 71.200 63.000 72.50 65.90 63.40 73.00 66.00 66.90 73.4 69.40
## CV residual -0.677 -0.338 2.47 -2.45 -1.88 3.33 3.82 -1.69 -3.4 -1.12
## 1385 836 1981 759 2408 2644 1472 2370 2823 2686
## Predicted 73.48 63.81 63.46 59.26 54.46 77.28 69.6 67.093 75.863 74.963
## cvpred 73.07 64.05 63.44 59.25 54.66 77.07 68.3 66.988 75.795 74.938
## Life.expectancy 65.20 57.90 61.80 61.30 56.00 72.30 73.2 67.600 75.400 74.500
## CV residual -7.87 -6.15 -1.64 2.05 1.34 -4.77 4.9 0.612 -0.395 -0.438
## 2915 2047 2156 1245 912 1977 1352 2407 2656 344
## Predicted 53.47 77.91 63.437 71.08 75.27 64.32 72.31 52.3 69.48 60.07
## cvpred 53.75 77.87 63.115 71.17 75.24 64.31 72.37 52.5 69.77 60.23
## Life.expectancy 52.60 75.50 63.800 66.80 67.90 62.70 67.80 54.9 71.00 57.50
## CV residual -1.15 -2.37 0.685 -4.37 -7.34 -1.61 -4.57 2.4 1.23 -2.73
## 112 640 2565 985 239 2272 1063 2034 285 460
## Predicted 71.31 74.74 68.38 71.59 71.30 73.869 68.09 67.88 60.39 70.693
## cvpred 71.31 74.68 68.42 71.68 71.15 73.651 68.07 68.08 60.38 70.533
## Life.expectancy 72.00 77.50 65.90 73.20 67.70 74.100 71.10 67.00 55.80 71.400
## CV residual 0.69 2.82 -2.52 1.52 -3.45 0.449 3.03 -1.08 -4.58 0.867
## 2853 1029 1870 2273 2676 2822 2051 2427 2058 1373
## Predicted 62.61 79.62 69.29 72.58 75.95 77.13 77.2 81.30 77.59 55.23
## cvpred 61.59 79.38 69.18 72.56 75.83 76.89 77.3 81.47 77.61 55.32
## Life.expectancy 69.90 86.00 72.50 74.00 74.20 75.40 74.9 82.60 86.00 54.10
## CV residual 8.31 6.62 3.32 1.44 -1.63 -1.49 -2.4 1.13 8.39 -1.22
## 2932 1479 1350 1563 678 1644 155 1549 1698 1097
## Predicted 52.51 63.6 71.3 63.29 77.42 78.781 70.7 78.377 72.77 57.76
## cvpred 52.34 63.3 71.5 63.31 77.44 78.729 70.8 78.453 72.83 57.75
## Life.expectancy 45.40 52.3 69.1 61.90 79.70 79.300 68.4 78.800 75.00 56.30
## CV residual -6.94 -11.0 -2.4 -1.41 2.26 0.571 -2.4 0.347 2.17 -1.45
## 483 1449 675 2641 820 2710 1545 2849 2288 829
## Predicted 60.74 77.18 77.51 74.66 71.58 61.55 77.38 68.49 71.265 71.221
## cvpred 60.76 77.22 77.82 74.58 71.49 60.55 77.49 68.52 71.423 71.174
## Life.expectancy 56.40 72.60 83.00 72.60 73.30 63.40 83.00 78.00 72.300 71.000
## CV residual -4.36 -4.62 5.18 -1.98 1.81 2.85 5.51 9.48 0.877 -0.174
## 2573 772 262 791 2917 983 599 1761 2060 573
## Predicted 71.05 71.87 70.68 72.5 52.42 72.97 64.78 68.57 78.34 73.565
## cvpred 71.14 71.78 70.63 72.5 52.51 72.81 64.75 68.56 78.29 73.811
## Life.expectancy 74.30 73.60 69.50 75.3 49.30 73.90 61.30 69.90 82.00 73.100
## CV residual 3.16 1.82 -1.13 2.8 -3.21 1.09 -3.45 1.34 3.71 -0.711
## 2635 2255 1035 2659 1897 356 1238 2911 1557 2926
## Predicted 72.462 62.40 81.10 70.77 49.17 74.205 69.45 61.46 67.50 56.014
## cvpred 72.558 62.36 80.76 70.93 48.45 74.063 69.57 61.51 67.37 55.971
## Life.expectancy 73.300 64.30 79.40 69.60 52.70 74.500 76.00 58.20 64.70 56.600
## CV residual 0.742 1.94 -1.36 -1.33 4.25 0.437 6.43 -3.31 -2.67 0.629
## 1382 515 1821 2439 199 1006 1214 571 689 1567
## Predicted 72.21 53.43 65.99 78.639 65.52 81.33 67.09 72.768 77.085 62.21
## cvpred 72.01 53.61 65.94 78.646 65.63 81.33 67.32 73.067 77.207 62.25
## Life.expectancy 65.70 49.90 67.00 79.500 69.50 79.10 65.30 73.900 78.100 59.90
## CV residual -6.31 -3.71 1.06 0.854 3.87 -2.23 -2.02 0.833 0.893 -2.35
## 950
## Predicted 65.5
## cvpred 65.5
## Life.expectancy 63.5
## CV residual -2.0
##
## Sum of squares = 2861 Mean square = 12.4 n = 231
##
## fold 3
## Observations in test set: 231
## 1980 259 1078 2256 1528 397 491 1675 295 1623
## Predicted 64.03 73.42 59.89 62.02 75.59 73.83 60.41 72.290 61.13 58.8
## cvpred 64.16 73.19 59.94 62.06 75.44 73.84 60.01 72.201 61.07 58.8
## Life.expectancy 62.00 69.80 58.40 63.50 72.40 72.00 52.80 72.700 67.40 56.8
## CV residual -2.16 -3.39 -1.54 1.44 -3.04 -1.84 -7.21 0.499 6.33 -2.0
## 202 588 2507 2671 136 455 1492 1656 1112 2732
## Predicted 65.22 70.80 79.76 76.19 80.30 70.25 59.84 62.248 66.727 72.42
## cvpred 65.14 70.77 79.48 75.91 80.51 70.15 59.98 62.342 66.772 71.91
## Life.expectancy 68.20 72.80 82.30 74.80 84.00 72.40 58.10 62.200 65.900 78.00
## CV residual 3.06 2.03 2.82 -1.11 3.49 2.25 -1.88 -0.142 -0.872 6.09
## 1588 25 1079 2711 900 2137 952 407 42 942
## Predicted 72.94 73.29 63.57 61.93 76.46 73.649 63.68 57.193 72.503 78.69
## cvpred 72.86 73.08 63.31 62.03 76.21 73.647 63.74 57.243 72.483 78.79
## Life.expectancy 74.80 75.90 58.10 63.30 69.70 73.000 62.30 56.900 73.400 82.00
## CV residual 1.94 2.82 -5.21 1.27 -6.51 -0.647 -1.44 -0.343 0.917 3.21
## 143 500 1579 2672 111 1194 408 1205 1736 2139
## Predicted 77.30 81.721 49.58 76.47 71.15 59.83 56.331 70.80 76.164 72.25
## cvpred 77.28 81.902 49.75 76.21 71.11 58.53 56.408 70.72 75.728 72.27
## Life.expectancy 78.60 81.600 48.50 74.70 72.60 65.50 56.100 68.70 75.600 69.60
## CV residual 1.32 -0.302 -1.25 -1.51 1.49 6.97 -0.308 -2.02 -0.128 -2.67
## 459 240 1294 2436 1081 948 52 2583 426 1594
## Predicted 68.76 70.98 80.89 76.97 58.30 66.354 59.71 68.52 55.96 72.38
## cvpred 68.66 71.07 80.81 76.68 58.34 66.311 59.83 68.48 56.05 72.32
## Life.expectancy 71.80 68.00 89.00 81.00 57.30 65.500 56.00 71.40 54.10 73.80
## CV residual 3.14 -3.07 8.19 4.32 -1.04 -0.811 -3.83 2.92 -1.95 1.48
## 1606 1310 1676 934 1869 1607 1467 144 2209 1309
## Predicted 72.56 69.65 72.41 78.02 69.59 71.75 72.48 77.12 69.79 71.08
## cvpred 72.29 69.65 72.34 77.73 69.56 71.51 72.21 77.09 69.58 71.05
## Life.expectancy 77.60 73.30 72.90 81.50 72.50 77.30 74.40 78.10 72.20 73.50
## CV residual 5.31 3.65 0.56 3.77 2.94 5.79 2.19 1.01 2.62 2.45
## 2648 1822 1252 121 2661 2685 2377 1192 871
## Predicted 73.86 65.782 81.156 82.63 73.29 74.8609 63.95 63.90 78.15
## cvpred 73.85 65.707 80.918 82.38 73.06 74.7436 64.12 63.13 78.05
## Life.expectancy 71.80 66.600 81.200 81.30 69.40 74.8000 65.80 66.40 76.10
## CV residual -2.05 0.893 0.282 -1.08 -3.66 0.0564 1.68 3.27 -1.95
## 1069 1362 406 1732 1036 2844 941 1601 2478 1988
## Predicted 69.893 69.75 57.709 66.19 78.43 68.60 78.8 72.093 71.1 61.38
## cvpred 69.694 69.92 57.754 66.38 78.16 68.55 78.9 72.052 71.1 61.58
## Life.expectancy 69.200 63.90 57.500 62.80 79.70 71.70 81.0 72.700 76.0 59.60
## CV residual -0.494 -6.02 -0.254 -3.58 1.54 3.15 2.1 0.648 4.9 -1.98
## 2501 131 2274 594 1065 270 233 1948 2011 1335
## Predicted 43.83 78.16 72.919 68.70 68.20 70.6 72.71 65.661 72.98 74.09
## cvpred 43.37 77.89 72.962 68.39 68.21 70.6 72.72 65.577 72.91 73.94
## Life.expectancy 45.60 81.10 73.800 63.20 76.00 68.5 69.80 65.100 74.90 73.60
## CV residual 2.23 3.21 0.838 -5.19 7.79 -2.1 -2.92 -0.477 1.99 -0.34
## 2400 797 1755 552 1624 342 102 1787 1236 21
## Predicted 56.61 72.26 70.1 76.43 58.08 64.58 71.76 61.91 67.8186 73.62
## cvpred 56.69 72.19 70.1 76.24 58.03 64.72 71.72 61.88 67.8468 73.49
## Life.expectancy 56.50 74.20 72.3 79.60 56.50 61.10 73.50 65.20 67.9000 76.60
## CV residual -0.19 2.01 2.2 3.36 -1.53 -3.62 1.78 3.32 0.0532 3.11
## 2643 566 2374 88 2219 585 1340 451 30 1625
## Predicted 72.866 73.89 63.52 77.15 66.909 71.66 75.24 73.273 72.87 57.86
## cvpred 72.654 73.69 63.52 77.02 66.741 71.62 75.08 72.981 72.68 57.81
## Life.expectancy 72.400 75.00 66.80 75.40 67.300 73.50 72.80 72.800 73.30 56.00
## CV residual -0.254 1.31 3.28 -1.62 0.559 1.88 -2.28 -0.181 0.62 -1.81
## 269 676 2646 576 2728 2561 998 1144 1879 93
## Predicted 72.94 76.40 72.299 70.2 52.81 68.41 77.38 69.89 56.56 77.13
## cvpred 72.75 76.25 72.172 69.9 52.88 68.37 77.19 69.79 56.54 76.93
## Life.expectancy 68.40 81.00 72.000 71.7 48.80 66.40 86.00 73.60 61.40 74.10
## CV residual -4.35 4.75 -0.172 1.8 -4.08 -1.97 8.81 3.81 4.86 -2.83
## 1874 1899 2251 831 2068 1360 2261 2566 114 1789
## Predicted 68.82 48.51 64.05 73.4 79.90 70.41 60.361 67.74 88.94 63.0
## cvpred 68.83 48.05 64.04 73.2 79.68 70.56 60.443 67.74 88.85 63.1
## Life.expectancy 76.00 52.00 66.40 69.9 77.30 64.70 59.700 65.20 82.70 64.5
## CV residual 7.17 3.95 2.36 -3.3 -2.38 -5.86 -0.743 -2.54 -6.15 1.4
## 858 1240 386 603 452 628 148 1968 648 1447
## Predicted 57.99 69.27 74.95 63.92 71.18 74.57 71.855 72.70 76.21 75.82
## cvpred 58.25 69.27 74.86 63.99 71.01 74.35 71.776 72.58 75.92 75.79
## Life.expectancy 67.00 76.00 74.30 60.00 72.70 79.40 71.900 76.40 76.30 73.60
## CV residual 8.75 6.73 -0.56 -3.99 1.69 5.05 0.124 3.82 0.38 -2.19
## 86 107 1209 124 1380 1548 1945 775 2828 2030
## Predicted 77.02 68.7 69.52 82.69 71.99 83.55 65.674 73.546 70.52 68.333
## cvpred 76.83 68.6 69.46 82.25 71.89 83.91 65.586 73.357 70.48 68.305
## Life.expectancy 75.50 73.0 67.90 86.00 66.10 79.40 66.000 73.100 69.20 68.000
## CV residual -1.33 4.4 -1.56 3.75 -5.79 -4.51 0.414 -0.257 -1.28 -0.305
## 98 758 399 44 951 1024 100 2562 1562 2226
## Predicted 73.71 59.76 76.01 73.54 64.28 63.72 72.25 68.49 63.42 66.030
## cvpred 73.51 59.85 75.85 73.36 64.36 63.48 72.19 68.46 63.45 65.999
## Life.expectancy 74.60 61.80 71.60 72.30 62.80 57.60 74.40 66.10 62.30 65.100
## CV residual 1.09 1.95 -4.25 -1.06 -1.56 -5.88 2.21 -2.36 -1.15 -0.899
## 2301 506 1792 1533 2564 418 2449 1660 1291 2292
## Predicted 60.7 78.90 62.507 76.24 68.14 63.06 71.582 62.23 81.831 69.35
## cvpred 60.8 78.64 62.592 76.32 68.12 63.06 71.506 62.32 81.774 69.29
## Life.expectancy 49.7 85.00 63.500 78.00 65.50 59.10 72.300 61.20 81.300 72.20
## CV residual -11.1 6.36 0.908 1.68 -2.62 -3.96 0.794 -1.12 -0.474 2.91
## 1831 1604 2018 600 1725 1241 1867 756 402 2553
## Predicted 81.8819 74.00 72.110 64.26 73.77 69.48 68.54 60.49 59.838 69.58
## cvpred 81.7847 73.63 72.049 64.25 73.53 69.48 68.38 60.55 59.893 69.57
## Life.expectancy 81.7000 78.20 72.800 61.00 65.90 74.00 73.20 62.70 59.300 72.60
## CV residual -0.0847 4.57 0.751 -3.25 -7.63 4.52 4.82 2.15 -0.593 3.03
## 2121 1529 2742 105 562 2500 1030 2448 2154 1791
## Predicted 75.99 77.33 72.22 71.25 73.90 45.00 79.49 71.400 64.975 62.47
## cvpred 75.94 77.33 72.26 71.21 73.68 44.52 79.27 71.336 64.862 62.54
## Life.expectancy 74.80 72.20 67.40 73.50 75.80 46.00 84.00 71.800 65.200 63.90
## CV residual -1.14 -5.13 -4.86 2.29 2.12 1.48 4.73 0.464 0.338 1.36
## 1769 503 798 326 1487 322 1589 1773 2305 339
## Predicted 60.53 78.83 72.21 73.87 42.20 74.56 72.51 51.790 56.4 67.83
## cvpred 60.12 78.53 72.12 73.65 42.42 74.31 72.41 51.924 56.7 67.87
## Life.expectancy 54.30 81.00 74.40 76.40 45.50 77.20 74.60 52.100 46.2 64.20
## CV residual -5.82 2.47 2.28 2.75 3.08 2.89 2.19 0.176 -10.5 -3.67
## 1559 1470 2609 1010 1825 1790 579 2690 875 1278
## Predicted 64.250 67.82 67.77 78.379 63.17 65.76 72.29 73.086 75.31 78.19
## cvpred 64.252 67.33 67.75 78.415 63.07 65.59 72.18 73.003 75.32 77.86
## Life.expectancy 63.800 73.70 66.20 78.000 64.70 64.20 74.40 73.200 73.00 81.00
## CV residual -0.452 6.37 -1.55 -0.415 1.63 -1.39 2.22 0.197 -2.32 3.14
## 644 1647 1540 785 1452 987 1483 32 1575
## Predicted 76.875 78.063 81.99 69.62 76.52 74.110 45.615 72.983 56.75
## cvpred 76.804 77.974 82.22 69.58 76.58 73.838 45.888 72.788 56.76
## Life.expectancy 77.700 78.500 81.70 71.20 75.00 74.400 46.200 72.600 54.10
## CV residual 0.896 0.526 -0.52 1.62 -1.58 0.562 0.312 -0.188 -2.66
## 551 2576 2705 1303 331 467 1394 2134 2009 505
## Predicted 76.44 73.450 61.03 71.77 65.91 66.68 61.72 72.2 73.4 82.09
## cvpred 76.24 73.209 61.16 71.69 65.47 66.59 61.69 72.3 73.3 82.05
## Life.expectancy 79.30 73.700 64.50 75.20 75.00 67.80 64.10 78.0 75.3 85.00
## CV residual 3.06 0.491 3.34 3.51 9.53 1.21 2.41 5.7 2.0 2.95
## 423 646 2681
## Predicted 59.13 77.955 73.608
## cvpred 59.23 77.791 73.513
## Life.expectancy 56.20 77.000 72.900
## CV residual -3.03 -0.791 -0.613
##
## Sum of squares = 2584 Mean square = 11.2 n = 231
##
## fold 4
## Observations in test set: 231
## 55 24 2908 469 643 1474 238 1082 34 2837
## Predicted 56.37 73.76 64.17 69.06 76.961 68.45 71.26 61.6 76.36 70.06
## cvpred 56.49 73.88 64.12 69.37 77.298 68.55 71.11 62.0 76.57 69.97
## Life.expectancy 49.10 75.30 61.10 67.00 77.800 72.70 67.20 56.8 75.40 67.30
## CV residual -7.39 1.42 -3.02 -2.37 0.502 4.15 -3.91 -5.2 -1.17 -2.67
## 2141 2369 109 16 1681 1693 638 1817 1014 488
## Predicted 71.52 66.03 70.77 57.68 71.067 73.42 75.15 66.66 65.85 57.05
## cvpred 71.44 66.09 70.72 57.96 70.928 73.34 75.33 67.01 65.83 56.96
## Life.expectancy 68.40 68.00 72.70 54.80 71.500 75.80 78.00 68.90 61.60 54.20
## CV residual -3.04 1.91 1.98 -3.16 0.572 2.46 2.67 1.89 -4.23 -2.76
## 1448 2202 2582 914 687 2055 554 1384 1784 855
## Predicted 79.07 72.63 68.96 68.83 75.87 76.4 76.65 72.3 66.93 58.25
## cvpred 79.41 72.76 68.84 68.84 76.05 76.5 76.59 72.2 67.07 58.21
## Life.expectancy 72.80 73.80 71.70 67.70 78.40 73.7 78.90 65.3 65.90 62.90
## CV residual -6.61 1.04 2.86 -1.14 2.35 -2.8 2.31 -6.9 -1.17 4.69
## 944 2042 1536 327 2477 945 2 1355 1654 1678
## Predicted 79.317 76.200 78.66 72.14 71.086 80.30 63.37 71.87 64.01 71.830
## cvpred 78.955 76.711 78.94 72.56 71.112 80.39 63.68 71.55 64.39 71.711
## Life.expectancy 79.200 77.100 71.40 76.10 71.300 79.00 59.90 65.30 62.70 72.100
## CV residual 0.245 0.389 -7.54 3.54 0.188 -1.39 -3.78 -6.25 -1.69 0.389
## 800 2839 861 2835 2070 1881 2936 1991 1345 1882
## Predicted 71.85 69.90 58.536 70.05 78.52 56.23 48.2 60.040 74.62 55.88
## cvpred 71.73 69.81 58.884 70.03 79.01 56.54 48.2 59.864 74.69 56.19
## Life.expectancy 73.60 67.20 59.400 67.80 76.90 63.00 44.8 58.900 71.90 59.40
## CV residual 1.87 -2.61 0.516 -2.23 -2.11 6.46 -3.4 -0.964 -2.79 3.21
## 956 1595 152 773 1653 1950 122 627 2637 2260
## Predicted 61.787 72.19 71.26 71.2 65.24 64.330 86.37 74.59 74.001 60.52
## cvpred 61.576 72.04 71.18 71.2 65.52 64.446 86.48 74.82 73.937 60.58
## Life.expectancy 61.400 73.70 73.00 73.4 63.00 64.600 81.20 79.50 73.000 65.00
## CV residual -0.176 1.66 1.82 2.2 -2.52 0.154 -5.28 4.68 -0.937 4.42
## 590 1611 1339 1349 1121 1671 1612 1143 2912 2216
## Predicted 70.980 71.15 76.70 75.74 67.18 73.596 71.56 69.94 60.63 74.52
## cvpred 70.913 71.32 76.87 75.79 67.08 73.518 71.73 70.14 60.51 74.51
## Life.expectancy 71.800 75.40 73.00 69.50 65.40 73.900 75.00 73.90 58.00 72.00
## CV residual 0.887 4.08 -3.87 -6.29 -1.68 0.382 3.27 3.76 -2.51 -2.51
## 2623 1076 106 2162 2035 517 1149 1068 1482 2847
## Predicted 62.08 60.17 70.72 62.25 68.386 52.79 68.93 70.408 47.720 68.51
## cvpred 62.08 60.36 70.64 62.59 68.248 52.74 69.02 70.663 47.378 68.53
## Life.expectancy 57.40 58.10 72.90 55.30 67.300 49.80 72.50 69.700 47.800 71.20
## CV residual -4.68 -2.26 2.26 -7.29 -0.948 -2.94 3.48 -0.963 0.422 2.67
## 1800 2375 2019 2740 3 1578 1883 2409 1969 2838
## Predicted 66.84 67.077 72.057 72.05 63.4 50.359 53.7 56.470 73.31 70.10
## cvpred 66.94 67.346 71.947 71.91 63.7 49.863 54.1 56.311 73.33 70.01
## Life.expectancy 65.80 66.500 72.200 67.70 59.9 50.000 58.2 57.300 76.20 67.80
## CV residual -1.14 -0.846 0.253 -4.21 -3.8 0.137 4.1 0.989 2.87 -2.21
## 2302 1955 2647 251 1457 2704 2608 1376 1778 1949
## Predicted 59.7 62.697 73.92 79.07 74.59 61.22 68.28 52.13 49.9438 65.188
## cvpred 60.0 62.706 73.78 79.36 74.64 61.34 68.19 51.82 49.8503 65.235
## Life.expectancy 48.9 63.500 71.90 78.90 69.90 65.60 66.60 52.10 49.8000 64.800
## CV residual -11.1 0.794 -1.88 -0.46 -4.74 4.26 -1.59 0.28 -0.0503 -0.435
## 2482 1655 354 910 1680 1863 1466 1273 205
## Predicted 72.73 63.60 74.6449 72.21 71.408 70.30 74.2685 78.62 64.07
## cvpred 72.84 63.96 74.8181 71.94 71.253 70.55 74.4213 78.64 64.06
## Life.expectancy 69.50 62.50 74.8000 68.10 71.500 74.50 74.5000 81.50 66.80
## CV residual -3.34 -1.46 -0.0181 -3.84 0.247 3.95 0.0787 2.86 2.74
## 937 405 649 2913 275 2041 1375 2215 936 1697
## Predicted 80.698 58.076 76.741 59.39 63.30 79.04 52.073 71.77 75.97 72.70
## cvpred 80.725 58.216 76.975 59.25 63.38 79.42 51.807 71.61 76.35 72.61
## Life.expectancy 81.100 58.100 76.000 57.40 59.50 77.30 52.400 75.00 81.30 75.00
## CV residual 0.375 -0.116 -0.975 -1.85 -3.88 -2.12 0.593 3.39 4.95 2.39
## 586 1391 1757 1446 2049 630 2300 2551 574 2503 1206
## Predicted 71.07 61.1 67.95 76.09 76.10 75.1 66.4 69.63 73.099 36.3 70.63
## cvpred 71.07 61.8 68.06 76.27 76.28 75.3 67.1 69.58 73.236 35.5 70.55
## Life.expectancy 73.10 64.7 71.40 73.80 75.20 79.0 54.0 72.80 72.700 46.4 68.50
## CV residual 2.03 2.9 3.34 -2.47 -1.08 3.7 -13.1 3.22 -0.536 10.9 -2.05
## 1271 790 2437 2745 2552 1983 2723 17 1776 149
## Predicted 80.08 72.54 80.169 71.50 69.63 66.80 61.60 74.58 49.97 71.5221
## cvpred 80.01 72.63 80.366 71.27 69.57 67.03 62.19 74.67 49.82 71.5055
## Life.expectancy 81.80 75.50 81.000 67.70 72.70 61.40 55.50 77.80 54.00 71.6000
## CV residual 1.79 2.87 0.634 -3.57 3.13 -5.63 -6.69 3.13 4.18 0.0945
## 254 997 1333 258 1944 828 2440 1751 1657
## Predicted 81.90 80.13 73.979 69.344 65.710 69.9 79.783 71.83 61.98428
## cvpred 82.16 80.64 74.035 69.455 65.781 69.9 79.933 71.92 61.99857
## Life.expectancy 78.00 86.00 73.900 70.000 66.200 75.0 79.400 73.90 62.00000
## CV residual -4.16 5.36 -0.135 0.545 0.419 5.1 -0.533 1.98 0.00143
## 1007 2557 1218 2819 2493 2397 2674 1016 2567 11
## Predicted 80.03 69.03 68.7 75.749 58.33 68.68 76.31 64.48 67.32 61.08
## cvpred 80.04 69.12 68.5 75.839 58.29 69.01 76.37 64.47 67.24 61.36
## Life.expectancy 78.50 68.80 66.3 75.400 56.50 59.20 74.60 69.00 64.30 57.30
## CV residual -1.54 -0.32 -2.2 -0.439 -1.79 -9.81 -1.77 4.53 -2.94 -4.06
## 575 2363 784 1687 1023 1672 2824 1300 404 2268
## Predicted 72.974 66.13 69.71 73.1 62.74 73.099 75.67 71.78 56.87 73.20
## cvpred 73.113 66.23 69.64 73.1 62.99 73.049 75.65 71.79 57.22 72.98
## Life.expectancy 72.200 68.80 71.40 76.3 57.90 73.600 75.40 75.80 58.60 75.30
## CV residual -0.913 2.57 1.76 3.2 -5.09 0.551 -0.25 4.01 1.38 2.32
## 1282 1060 2223 365 486 1386 2584 888 2161 639
## Predicted 78.632 67.81 68.98 75.10 63.66 73.32 68.84 58.31 58.317 73.20
## cvpred 78.556 67.91 69.22 75.07 63.96 73.79 68.65 58.63 58.057 73.29
## Life.expectancy 78.900 71.70 66.20 71.80 55.30 65.10 71.20 61.80 57.600 78.30
## CV residual 0.344 3.79 -3.02 -3.27 -8.66 -8.69 2.55 3.17 -0.457 5.01
## 343 2854 2290 1353 2048 2069 1381 1153 328 2016
## Predicted 62.71 62.81 71.405 72.82 75.987 80.18 72.2 67.87 73.41 71.20
## cvpred 62.45 63.07 71.213 72.59 76.186 80.56 72.1 67.88 73.59 71.22
## Life.expectancy 59.20 69.60 72.200 67.80 75.300 77.20 65.8 71.30 76.00 74.00
## CV residual -3.25 6.53 0.987 -4.79 -0.886 -3.36 -6.3 3.42 2.41 2.78
## 2159 1196 1694 2142 1574 645 6 2818 1558 156
## Predicted 62.07 65.24 73.62 71.81 64.7 78.05 62.74 74.41 62.66 70.63
## cvpred 62.22 65.89 73.56 71.75 65.3 78.45 63.06 74.63 62.84 70.72
## Life.expectancy 68.00 64.80 75.30 68.20 55.3 77.10 58.80 76.40 64.30 68.40
## CV residual 5.78 -1.09 1.74 -3.55 -10.0 -1.35 -4.26 1.77 1.46 -2.32
## 1198 2267 1762 330 1346 1995 2938 685 2813 1779
## Predicted 64.26 72.88 70.211 74.5 74.34 70.20 38.11 76.76 75.925 55.47
## cvpred 64.67 72.72 70.302 74.8 74.41 70.02 37.43 76.96 76.074 55.73
## Life.expectancy 64.00 75.40 69.500 75.7 71.70 73.60 46.00 78.60 76.800 49.50
## CV residual -0.67 2.68 -0.802 0.9 -2.71 3.58 8.57 1.64 0.726 -6.23
## 2622 1152 2028 939 84 2032 2548 1987 580 1147
## Predicted 67.46 67.01 68.03699 76.9 79.17 68.182 68.74 60.58 72.98 71.37
## cvpred 67.76 67.12 68.00559 76.6 79.22 68.104 68.85 60.75 73.02 71.64
## Life.expectancy 58.30 71.60 68.00000 89.0 75.90 67.500 73.50 59.90 74.30 73.00
## CV residual -9.46 4.48 -0.00559 12.4 -3.32 -0.604 4.65 -0.85 1.28 1.36
## 1699 1388 2845 2724 2703 2816 1477 635 428 1734
## Predicted 72.53 69.96 68.5 61.53 61.51 77.006 58.00 75.16 53.75 77.51
## cvpred 72.39 69.67 68.5 62.14 61.63 77.059 58.03 75.31 53.83 77.62
## Life.expectancy 74.80 65.00 71.6 54.90 65.80 76.300 52.10 78.00 52.60 75.90
## CV residual 2.41 -4.67 3.1 -7.24 4.17 -0.759 -5.93 2.69 -1.23 -1.72
## 2935 56
## Predicted 39.21 57.13
## cvpred 38.58 57.08
## Life.expectancy 44.50 48.70
## CV residual 5.92 -8.38
##
## Sum of squares = 3308 Mean square = 14.3 n = 231
##
## fold 5
## Observations in test set: 231
## 1999 2286 569 647 1572 1034 1691 1077 2270 346
## Predicted 70.32 71.27 73.499 75.27 60.78 79.533 73.01 60.36 73.662 57.75
## cvpred 70.31 71.43 73.577 75.14 60.61 79.674 72.97 60.32 73.652 57.69
## Life.expectancy 72.70 72.60 74.400 76.60 57.60 79.900 75.60 58.80 74.600 54.80
## CV residual 2.39 1.17 0.823 1.46 -3.01 0.226 2.63 -1.52 0.948 -2.89
## 1598 400 41 905 2431 116 125 1494 90 591
## Predicted 72.698 73.89 71.09 75.8 79.50 88.41 84.12 60.67 76.95 69.28
## cvpred 72.661 73.74 71.08 76.0 79.29 88.76 84.19 60.57 77.07 68.99
## Life.expectancy 73.200 71.10 73.80 68.9 81.90 82.30 83.00 67.00 75.20 71.50
## CV residual 0.539 -2.64 2.72 -7.1 2.61 -6.46 -1.19 6.43 -1.87 2.51
## 1994 827 1343 1253 2153 2833 1621 2604 1341 2444
## Predicted 70.13 72.53 74.87 81.2222 68.19 69.05 59.39 68.75 75.15 72.14
## cvpred 70.25 72.66 74.75 81.0859 68.37 69.01 59.34 68.82 75.01 72.13
## Life.expectancy 73.80 71.20 72.30 81.0000 65.70 68.00 57.30 67.70 72.40 74.60
## CV residual 3.55 -1.46 -2.45 -0.0859 -2.67 -1.01 -2.04 -1.12 -2.61 2.47
## 1387 2126 1040 1368 2547 1758 255 1256 1990 2683
## Predicted 71.17 75.60 76.89 60.7 69.04 69.48 84.17 82.86 60.53 76.363
## cvpred 70.99 75.46 76.86 60.5 68.76 69.52 84.25 82.89 60.32 76.404
## Life.expectancy 65.00 73.10 79.00 63.0 73.70 71.00 78.00 86.00 59.10 75.500
## CV residual -5.99 -2.36 2.14 2.5 4.94 1.48 -6.25 3.11 -1.22 -0.904
## 2502 2605 2071 1304 2693 1334 799 1038 246 249
## Predicted 44.48 68.86 77.74 70.62 72.471 73.745 72.09 77.28 77.95 77.27
## cvpred 44.79 68.94 77.69 70.59 72.417 73.592 72.07 77.31 77.93 77.02
## Life.expectancy 45.90 67.40 76.60 75.00 72.000 73.700 74.40 79.20 80.00 79.50
## CV residual 1.11 -1.54 -1.09 4.41 -0.417 0.108 2.33 1.89 2.07 2.48
## 420 284 1039 1119 1580 2125 2505 2653 1971 38
## Predicted 62.49 60.2 78.109 65.315 48.42 76.62 39.04 71.63 73.6 74.019
## cvpred 62.57 60.2 78.216 65.058 48.36 76.51 38.98 71.59 73.6 74.014
## Life.expectancy 58.00 56.1 79.100 65.300 47.10 73.40 48.40 78.00 75.8 74.700
## CV residual -4.57 -4.1 0.884 0.242 -1.26 -3.11 9.42 6.41 2.2 0.686
## 1458 1276 2138 304 532 2003 1824 1764 2744 419
## Predicted 74.19 78.73 73.43 57.96 53.92 70.50 67.59 69.349 72.06 67.02
## cvpred 74.01 78.59 73.43 58.54 53.69 70.59 67.74 69.508 72.09 67.31
## Life.expectancy 71.00 84.00 70.00 62.00 51.80 71.90 65.40 68.600 67.60 58.60
## CV residual -3.01 5.41 -3.43 3.46 -1.89 1.31 -2.34 -0.908 -4.49 -8.71
## 274 1636 2924 2046 2054 1767 1111 2925 348 2722
## Predicted 63.68 77.41 59.376 76.766 76.75 62.81 66.84 58.152 48.910 61.98
## cvpred 63.74 77.09 59.418 76.637 76.59 63.06 66.83 58.188 48.755 62.33
## Life.expectancy 59.70 81.40 59.200 75.700 74.20 55.30 65.60 58.000 48.100 56.30
## CV residual -4.04 4.31 -0.218 -0.937 -2.39 -7.76 -1.23 -0.188 -0.655 -6.03
## 1537 1269 338 519 1600 2696 2130 1306 2814 982
## Predicted 77.97 80.32 68.51 52.14 74.07 73.68 74.35 71.91 75.96 74.642
## cvpred 77.96 80.34 68.35 51.98 74.11 73.75 74.19 71.86 75.93 74.674
## Life.expectancy 71.20 82.10 65.10 48.60 72.90 78.00 71.90 74.50 76.50 74.200
## CV residual -6.76 1.76 -3.25 -3.38 -1.21 4.25 -2.29 2.64 0.57 -0.474
## 1211 1771 2651 198 358 2738 1730 410 2157 1880
## Predicted 71.04 59.92 71.69 66.04 74.023 70.28 67.69 58.93 66.2 56.5
## cvpred 71.07 60.26 71.65 66.12 74.092 70.01 67.63 59.26 66.6 56.5
## Life.expectancy 67.50 53.80 71.10 69.90 73.800 67.70 63.80 54.30 62.8 69.0
## CV residual -3.57 -6.46 -0.55 3.78 -0.292 -2.31 -3.83 -4.96 -3.8 12.5
## 141 1268 403 1964 1019 1301 679 2140 1722 2848
## Predicted 76.49 81.170 62.76 72.66 66.51 71.70 77.20 71.85 74.50 68.7
## cvpred 76.46 81.226 63.09 72.57 66.69 71.63 77.02 71.83 74.73 68.6
## Life.expectancy 78.80 82.200 59.00 77.30 59.90 75.60 79.50 69.40 66.30 71.0
## CV residual 2.34 0.974 -4.09 4.73 -6.79 3.97 2.48 -2.43 -8.43 2.4
## 363 1197 2496 357 1641 2508 2020 1989 1453 1984
## Predicted 74.1 62.21 53.359 74.259 77.0 79.85 72.656 61.02 76.015 62.63
## cvpred 74.1 62.68 53.563 74.305 76.7 79.46 72.748 60.81 75.858 62.58
## Life.expectancy 72.7 64.40 52.600 74.100 82.0 81.90 72.100 59.30 76.000 61.10
## CV residual -1.4 1.72 -0.963 -0.205 5.3 2.44 -0.648 -1.51 0.142 -1.48
## 2574 1583 778 325 1550 1739 1461 2669 2735 104
## Predicted 71.63 46.63 70.53 73.50 82.19 75.162 73.9 76.49 73.9 72.09
## cvpred 71.74 46.63 70.57 73.42 82.48 75.166 73.7 76.58 73.8 72.16
## Life.expectancy 74.10 44.60 73.30 76.90 78.70 75.000 74.9 74.90 75.0 73.20
## CV residual 2.36 -2.03 2.73 3.48 -3.78 -0.166 1.2 -1.68 1.2 1.04
## 10 1374 2452 2581 2285 1450 2721 1293 859 794
## Predicted 61.08 53.399 72.04 69.7 72.318 76.31 57.4302 81.26 57.80 72.49
## cvpred 60.98 53.356 72.04 69.8 72.197 76.15 57.5586 81.22 57.78 72.52
## Life.expectancy 57.30 53.000 74.20 71.6 72.700 71.90 57.5000 88.00 62.00 74.60
## CV residual -3.68 -0.356 2.16 1.8 0.503 -4.25 -0.0586 6.78 4.22 2.08
## 142 227 890 2062 1008 1688 2368 1332 473 2026
## Predicted 80.71 76.61 56.14 78.12 78.641 71.78 66.45 73.681 68.02 68.0461
## cvpred 80.95 76.92 56.25 78.27 78.667 71.77 66.45 73.546 68.28 68.0004
## Life.expectancy 78.70 71.70 59.80 79.30 78.400 76.10 68.10 74.000 65.00 68.1000
## CV residual -2.25 -5.22 3.55 1.03 -0.267 4.33 1.65 0.454 -3.28 0.0996
## 1003 135 91 103 514 2211 2454 874 1617 1444
## Predicted 82.31 81.447 77.04 70.04 54.10 73.67 71.9 75.07 70.51 76.04
## cvpred 82.64 81.442 77.14 69.99 53.94 73.68 71.9 75.24 70.63 75.71
## Life.expectancy 79.80 82.000 74.90 73.30 58.00 71.60 73.9 74.20 78.00 74.40
## CV residual -2.84 0.558 -2.24 3.31 4.06 -2.08 2.0 -1.04 7.37 -1.31
## 456 1637 1020 368 323 1871 1547 2135 1061 2483
## Predicted 70.14 77.21 61.71 74.708 75.57 71.43 76.42 72.06 68.21 69.778
## cvpred 70.34 76.91 61.69 74.823 75.55 71.56 76.16 71.96 68.14 69.679
## Life.expectancy 72.40 81.10 59.40 75.000 77.00 73.00 79.70 77.00 71.40 69.300
## CV residual 2.06 4.19 -2.29 0.177 1.45 1.44 3.54 5.04 3.26 -0.379
## 2559 1834 873 261 2673 157 2277 760 2229 291
## Predicted 68.98 79.97 76.07 70.370 76.14 70.44 73.403 59.0 65.51 68.068
## cvpred 68.93 79.95 76.26 70.397 76.27 70.27 73.397 58.8 65.54 68.135
## Life.expectancy 67.30 81.10 74.90 69.400 74.70 67.80 73.000 69.0 63.80 69.100
## CV residual -1.63 1.15 -1.36 -0.997 -1.57 -2.47 -0.397 10.2 -1.74 0.965
## 2398 2642 1685 993 876 2680 1613 2826 1729 1371
## Predicted 62.23 72.718 73.01 72.362 74.76 75.39 71.97 73.43 66.92 58.03
## cvpred 62.03 72.739 72.93 72.279 74.97 75.57 71.98 73.15 66.81 58.05
## Life.expectancy 58.90 72.500 76.60 73.000 73.00 73.20 74.30 75.10 64.00 56.80
## CV residual -3.13 -0.239 3.67 0.721 -1.97 -2.37 2.32 1.95 -2.81 -1.25
## 1866 2858 2057 2404 2701 280 1190 1359 2306 2815 2655
## Predicted 68.7 64.34 76.9 51.02 71.21 61.64 72.5 70.7 61.9 76.069 69.8
## cvpred 68.7 65.29 76.7 50.98 71.36 61.69 72.9 70.7 62.3 76.068 69.4
## Life.expectancy 74.5 69.00 89.0 53.80 65.60 57.60 67.3 64.4 45.3 77.000 74.0
## CV residual 5.8 3.71 12.3 2.82 -5.76 -4.09 -5.6 -6.3 -17.0 0.932 4.6
## 57 393 1451 26 530 2146 2914 1116 1801 1460
## Predicted 56.70 72.521 75.94 70.29 55.09 70.83 63.21 71.22 64.610 73.72
## cvpred 56.79 72.365 75.76 70.29 54.94 70.88 63.51 71.47 64.528 73.55
## Life.expectancy 48.20 72.600 78.00 74.20 52.60 65.00 55.70 65.20 64.300 74.80
## CV residual -8.59 0.235 2.24 3.91 -2.34 -5.88 -7.81 -6.27 -0.228 1.25
## 290 1986 1296 1037 82 1875 629 2649 1596 1365
## Predicted 68.13 66.08 79.853 77.02 77.3 68.53 75.47 74.26 72.55 63.374
## cvpred 68.21 66.18 79.758 77.13 77.5 68.55 75.43 74.31 72.51 63.399
## Life.expectancy 69.40 64.00 80.000 79.30 76.2 75.00 79.20 71.60 73.60 62.600
## CV residual 1.19 -2.18 0.242 2.17 -1.3 6.45 3.77 -2.71 1.09 -0.799
## 1383 19 1498 1661 1750 1645 1568 2376 2667 2129
## Predicted 72.35 74.5 62.46 61.87 71.81 79.2128 62.01 63.60 74.683 74.61
## cvpred 72.64 74.6 62.44 61.82 71.84 79.0373 61.95 63.56 74.754 74.47
## Life.expectancy 65.50 77.2 58.60 69.00 74.10 79.0000 59.30 66.20 75.100 72.50
## CV residual -7.14 2.6 -3.84 7.18 2.26 -0.0373 -2.65 2.64 0.346 -1.97
##
## Sum of squares = 3245 Mean square = 14.1 n = 231
##
## Overall (Sum over all 231 folds)
## ms
## 12.6mean((data.test$Life.expectancy - predict(model.selected, data.test)) ^ 2)## [1] 13.5VIF for the additive model
vif(model.additive)## Year StatusDeveloping
## 1.16 1.83
## Adult.Mortality infant.deaths
## 1.71 261.01
## Alcohol percentage.expenditure
## 2.36 10.34
## Hepatitis.B Measles
## 1.66 1.54
## BMI under.five.deaths
## 1.73 254.12
## Polio Total.expenditure
## 1.69 1.12
## Diphtheria HIV.AIDS
## 2.06 1.42
## GDP Population
## 10.95 1.91
## thinness..1.19.years thinness.5.9.years
## 8.59 8.69
## Income.composition.of.resources Schooling
## 3.06 3.67which(vif(model.additive) > 5)## infant.deaths percentage.expenditure under.five.deaths
## 4 6 10
## GDP thinness..1.19.years thinness.5.9.years
## 15 17 18vif(model.selected)## Year StatusDeveloping
## 1.12 1.81
## Adult.Mortality infant.deaths
## 1.68 242.78
## Alcohol percentage.expenditure
## 2.31 1.39
## BMI under.five.deaths
## 1.52 244.30
## Total.expenditure Diphtheria
## 1.12 1.24
## HIV.AIDS Income.composition.of.resources
## 1.41 3.03
## Schooling
## 3.57which(vif(model.selected) > 5)## infant.deaths under.five.deaths
## 4 8The selected model efficiently removed some predictors which have colinearity issues, but not all. We can see infant.deaths and under.five.deaths are still co-exist in the selected model.
plot(infant.deaths ~ under.five.deaths, data = data)
Model Building
# train test split 70/30 hold out
set.seed(42)
train_size = floor(0.7 * nrow(data))
train_idx = sample(nrow(data), train_size)
data_trn = data[train_idx, ]
data_tst = data[-train_idx, ]# Define functions
calc_loocv_rmse = function(model) {
c("LOOCV_RMSE:",sqrt(mean((resid(model) / (1 - hatvalues(model))) ^ 2)))
}
calc_bp = function(model) {
c("BP test:", unname(bptest(model)$p.value))
}
calc_shapiro = function(model) {
c("Shapiro test:", unname(shapiro.test(resid(model))$p.value))
}
calc_adj_r2 = function(model) {
c("Adj.R2:", summary(model)$adj.r.squared)
}# Model_1, basic additive model with all the parameters
model_1 = lm(Life.expectancy ~ ., data_trn)
par(mfrow=c(2,2))
plot(model_1)
calc_bp(model_1)## [1] "BP test:" "1.06753304313199e-18"calc_shapiro(model_1)## [1] "Shapiro test:" "0.000142390687235932"calc_loocv_rmse(model_1)## [1] "LOOCV_RMSE:" "3.58422898173348"calc_adj_r2(model_1)## [1] "Adj.R2:" "0.831530797195294"# Model_2, backward AIC on additive model
model_2 = step(model_1, trace = FALSE)
coef(model_2)## (Intercept) Year
## 286.6524 -0.1166
## StatusDeveloping Adult.Mortality
## -0.7627 -0.0148
## infant.deaths Alcohol
## 0.0793 -0.1400
## percentage.expenditure BMI
## 0.0005 0.0338
## under.five.deaths Polio
## -0.0597 0.0108
## Total.expenditure Diphtheria
## 0.1513 0.0136
## HIV.AIDS thinness..1.19.years
## -0.4572 -0.0626
## Income.composition.of.resources Schooling
## 10.6011 0.8706par(mfrow=c(2,2))
plot(model_2)
calc_bp(model_2)## [1] "BP test:" "5.89766168948721e-20"calc_shapiro(model_2)## [1] "Shapiro test:" "0.000152257737050676"calc_loocv_rmse(model_2)## [1] "LOOCV_RMSE:" "3.57398562547131"calc_adj_r2(model_2)## [1] "Adj.R2:" "0.832143041393922"# Model_3, backward BIC on additive model
n = length(resid(model_1))
model_3 = step(model_1, k = log(n), trace = FALSE)
coef(model_3)## (Intercept) Year
## 299.26327 -0.12352
## Adult.Mortality infant.deaths
## -0.01516 0.07874
## Alcohol percentage.expenditure
## -0.09713 0.00053
## BMI under.five.deaths
## 0.03721 -0.06008
## Total.expenditure Diphtheria
## 0.16017 0.01873
## HIV.AIDS Income.composition.of.resources
## -0.46262 10.77947
## Schooling
## 0.90100par(mfrow=c(2,2))
plot(model_3)
calc_bp(model_3)## [1] "BP test:" "4.75415871100533e-22"calc_shapiro(model_3)## [1] "Shapiro test:" "0.0000389851564983809"calc_loocv_rmse(model_3)## [1] "LOOCV_RMSE:" "3.58063093482768"calc_adj_r2(model_3)## [1] "Adj.R2:" "0.831059196901044"We can see that no big improvement on AIC and BIC results based on the additive model.
Next, we will start with the interactive model.
# Model_4, basic interactive model with all the parameters
model_4 = lm(Life.expectancy ~ . ^ 2, data_trn)
par(mfrow=c(2,2))
plot(model_4)## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
calc_bp(model_4)## [1] "BP test:" "0.0350257273124796"calc_shapiro(model_4)## [1] "Shapiro test:" "2.00075047432031e-14"calc_loocv_rmse(model_4)## [1] "LOOCV_RMSE:" "6.32632579517486"calc_adj_r2(model_4)## [1] "Adj.R2:" "0.907962924404157"length(coef(model_4))## [1] 211We can see that the interactive model using all the predictors turns out really big and there are 211 parameters in the model. We will focus on the parameters that are selected by Model_2 and apply AIC on the interactive model based on those parameters.
# Model_5, interactive model based on Model_2
# under.five.deaths is excluded because the colinearity issue with infant.deanths parameters
coef(model_2)## (Intercept) Year
## 286.6524 -0.1166
## StatusDeveloping Adult.Mortality
## -0.7627 -0.0148
## infant.deaths Alcohol
## 0.0793 -0.1400
## percentage.expenditure BMI
## 0.0005 0.0338
## under.five.deaths Polio
## -0.0597 0.0108
## Total.expenditure Diphtheria
## 0.1513 0.0136
## HIV.AIDS thinness..1.19.years
## -0.4572 -0.0626
## Income.composition.of.resources Schooling
## 10.6011 0.8706model_5 = lm(Life.expectancy ~ (Year + Status + Adult.Mortality + infant.deaths + Alcohol + percentage.expenditure + BMI + Polio + Total.expenditure
+ Diphtheria + HIV.AIDS + thinness..1.19.years + Income.composition.of.resources + Schooling) ^ 2, data = data_trn)
par(mfrow=c(2,2))
plot(model_5)
calc_bp(model_5)## [1] "BP test:" "4.1462009319212e-07"calc_shapiro(model_5)## [1] "Shapiro test:" "3.83717678229168e-11"calc_loocv_rmse(model_5)## [1] "LOOCV_RMSE:" "3.00964718488528"calc_adj_r2(model_5)## [1] "Adj.R2:" "0.895169999246715"length(coef(model_5))## [1] 106Model_5 has lower BP and Shapiro test results compared to the first 3 models, however, there are still 106 parameters in the model. We will use AIC and BIC to reduce the model.
# Model_6, backward AIC on interactive model
model_6 = step(model_5, trace = FALSE)
par(mfrow=c(2,2))
plot(model_5)
calc_bp(model_5)## [1] "BP test:" "4.1462009319212e-07"calc_shapiro(model_5)## [1] "Shapiro test:" "3.83717678229168e-11"calc_loocv_rmse(model_5)## [1] "LOOCV_RMSE:" "3.00964718488528"calc_adj_r2(model_5)## [1] "Adj.R2:" "0.895169999246715"# Model_7, backward BIC on interactive model
n = length(resid(model_5))
model_7 = step(model_5, k = log(n), trace = FALSE)
par(mfrow=c(2,2))
plot(model_7)
calc_bp(model_7)## [1] "BP test:" "6.43673809602792e-12"calc_shapiro(model_7)## [1] "Shapiro test:" "1.3729812233272e-10"calc_loocv_rmse(model_7)## [1] "LOOCV_RMSE:" "2.92111619240649"calc_adj_r2(model_7)## [1] "Adj.R2:" "0.890358899035256"We can see that model_7 still have 39 parameters. To simply the model, we can use p-value < 0.0001 to filter predictors. We will also add second order predictors and use AIC/BIC to further reduce model.
length(coef(model_7))## [1] 39which(summary(model_7)$coefficients[,4] < 0.0001)## Adult.Mortality
## 4
## BMI
## 8
## Diphtheria
## 11
## thinness..1.19.years
## 13
## Income.composition.of.resources
## 14
## Schooling
## 15
## Year:Income.composition.of.resources
## 18
## Year:Schooling
## 19
## StatusDeveloping:Adult.Mortality
## 20
## StatusDeveloping:thinness..1.19.years
## 22
## Adult.Mortality:Schooling
## 25
## infant.deaths:Income.composition.of.resources
## 26
## infant.deaths:Schooling
## 27
## Alcohol:Total.expenditure
## 28
## Alcohol:HIV.AIDS
## 29
## Alcohol:Income.composition.of.resources
## 31
## BMI:Diphtheria
## 33
## BMI:Income.composition.of.resources
## 34
## BMI:Schooling
## 35
## Total.expenditure:Income.composition.of.resources
## 38model_8 = lm(Life.expectancy ~ Adult.Mortality + BMI + Diphtheria + thinness..1.19.years + Income.composition.of.resources + Schooling + Year:Income.composition.of.resources + Year:Schooling + Status:Adult.Mortality + Status:thinness..1.19.years + Adult.Mortality:Schooling + infant.deaths:Income.composition.of.resources + infant.deaths:Schooling + Alcohol:Total.expenditure + Alcohol:HIV.AIDS + Alcohol:Income.composition.of.resources + BMI:Diphtheria + BMI:Income.composition.of.resources + BMI:Schooling + Total.expenditure:Income.composition.of.resources + I(Adult.Mortality^2) + I(BMI^2) + I(Diphtheria^2) + I(thinness..1.19.years^2) + I(Income.composition.of.resources^2) + I(Schooling^2), data = data_trn)
length(coef(model_8))## [1] 27# Model_9, backward AIC on reduced model
model_9 = step(model_8, trace = FALSE)
par(mfrow=c(2,2))
plot(model_9)
calc_bp(model_9)## [1] "BP test:" "1.25586859508963e-17"calc_shapiro(model_9)## [1] "Shapiro test:" "1.43501270267459e-09"calc_loocv_rmse(model_9)## [1] "LOOCV_RMSE:" "3.01869412852157"calc_adj_r2(model_9)## [1] "Adj.R2:" "0.881224986529788"# Model_10, backward BIC on reduced model
n = length(resid(model_8))
model_10 = step(model_8, k = log(n), trace = FALSE)
par(mfrow=c(2,2))
plot(model_10)
calc_bp(model_10)## [1] "BP test:" "2.86982827390071e-17"calc_shapiro(model_10)## [1] "Shapiro test:" "2.48317788164929e-09"calc_loocv_rmse(model_10)## [1] "LOOCV_RMSE:" "3.02059894996611"calc_adj_r2(model_10)## [1] "Adj.R2:" "0.880949043095113"length(coef(model_10))## [1] 24There are still 24 parameters after BIC step.
Change strategy, use the first order predictors in model_8 to build the interactive and second order models and apply AIC/BIC on it.
model_11 = lm(Life.expectancy ~ (Adult.Mortality + BMI + Diphtheria + thinness..1.19.years + Income.composition.of.resources + Schooling) ^ 2 + I(Adult.Mortality^2) + I(BMI^2) + I(Diphtheria^2) + I(thinness..1.19.years^2) + I(Income.composition.of.resources^2) + I(Schooling^2), data = data_trn)
length(coef(model_11))## [1] 28# Model_12, backward AIC on reduced model_11
model_12 = step(model_11, trace = FALSE)
par(mfrow=c(2,2))
plot(model_12)
calc_bp(model_12)## [1] "BP test:" "9.32569415279849e-16"calc_shapiro(model_12)## [1] "Shapiro test:" "6.9418924612486e-16"calc_loocv_rmse(model_12)## [1] "LOOCV_RMSE:" "3.20536581835464"calc_adj_r2(model_12)## [1] "Adj.R2:" "0.866503456987311"length(coef(model_12))## [1] 20# Model_13, backward BIC on reduced model_11
n = length(resid(model_11))
model_13 = step(model_11, k = log(n), trace = FALSE)
par(mfrow=c(2,2))
plot(model_13)
calc_bp(model_13)## [1] "BP test:" "1.38613074491302e-18"calc_shapiro(model_13)## [1] "Shapiro test:" "3.08693987626621e-16"calc_loocv_rmse(model_13)## [1] "LOOCV_RMSE:" "3.21577815809087"calc_adj_r2(model_13)## [1] "Adj.R2:" "0.86449056663892"length(coef(model_13))## [1] 16